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Study Guides > ALGEBRA / TRIG I

Problem Set: Ratios, Rates, Probabilities, and Averages

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.
  1. 33 , 88 , 22 , 22 , 55

    Answer: 4

  2. 66 , 11 , 99 , 33 , 44 , 77
  3. 6565 , 1313 , 4848 , 3232 , 1919 , 3333

    Answer: 35

  4. 3434 , 4545 , 2929 , 6161 , and 4141
  5. 202202 , 241241 , 265265 , 274274

    Answer: 245.5

  6. 525525 , 532532 , 558558 , 574574
  7. 12.4512.45 , 12.9912.99 , 10.5010.50 , 11.2511.25 , 9.999.99 , 12.7212.72

    Answer: 11.65

  8. 28.828.8 , 32.932.9 , 32.532.5 , 27.927.9 , 30.430.4 , 32.532.5 , 31.631.6 , 32.732.7
  9. 2,4,1,0,1,and12,4,1,0,1,\text{and}1
  10. {$270} , {$310.50} , {$243.75} , and {$252.15}

    Answer: $269.10

  11. Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited 3,0,8,1,and83,0,8,1, and 8 minutes. Find the mean
  12. In the last three months, Raul’s water bills were {$31.45}, {$48.76},\text{and} {$42.60}. Find the mean.

    Answer: $40.94

Calculate the Mean of a Set of Numbers in Applications

In the following exercises, find the mean.
  1. Four girls leaving a mall were asked how much money they had just spent. The amounts were {$0} , {$14.95} , {$35.25} , and {$25.16} . Find the mean amount of money spent.

    Answer: $18.84

  2. Juan bought 55 shirts to wear to his new job. The costs of the shirts were {$32.95} , {$38.50} , {$30.00} , {$17.45} , and {$24.25} . Find the mean cost.
  3. The number of minutes it took Jim to ride his bike to school for each of the past six days was 2121 , 1818 , 1616 , 1919 , 2424 , and 1919 . Find the mean number of minutes.

    Answer: 19.5 minutes

  4. Norris bought six books for his classes this semester. The costs of the books were {$74.28} , {$120.95} , {$52.40} , {$10.59} , {$35.89} , and {$59.24} . Find the mean cost.
  5. The top eight hitters in a softball league have batting averages of .373.373 , .360.360 , .321.321 , .321.321 , .320.320 , .312.312 , .311.311 , and .311.311 . Find the mean of the batting averages. Round your answer to the nearest thousandth.

    Answer: 0.329

  6. The monthly snowfall at a ski resort over a six-month period was 60.360.3, 79.779.7, 50.950.9, 28.028.0, 47.447.4, and 46.146.1 inches. Find the mean snowfall.

Find the Median of a Set of Numbers

In the following exercises, find the median.
  1. 2424 , 1919 , 1818 , 2929 , 2121

    Answer: 21

  2. 4848 , 5151 , 4646 , 4242 , 5050
  3. 6565 , 5656 , 3535 , 3434 , 4444 , 3939 , 5555 , 5252 , 4545

    Answer: 45

  4. 121121 , 115115 , 135135 , 109109 , 136136 , 147147 , 127127 , 119119 , 110110
  5. 44 , 88 , 11 , 55 , 1414 , 33 , 11 , 1212

    Answer: 4.5

  6. 33 , 99 , 22 , 66 , 2020 , 33 , 33 , 1010
  7. 99.299.2 , 101.9101.9 , 98.698.6 , 99.599.5 , 100.8100.8 , 99.899.8

    Answer: 99.65

  8. 28.828.8 , 32.932.9 , 32.532.5 , 27.927.9 , 30.430.4 , 32.532.5 , 31.631.6 , 32.732.7
  9. 4141 , 4545 , 3232 , 6060 , 5858
  10. 2525 , 2323 , 2424 , 2626 , 2929 , 1919 , 1818 , 3232

    Answer: 24.5

Find the Median of a Set of Numbers in Applications

In the following exercises, find the median.
  1. Last week Ray recorded how much he spent for lunch each workday. He spent {$6.50} , {$7.25} , {$4.90} , {$5.30} , and {$12.00} . Find the median.

    Answer: $6.50

  2. Michaela is in charge of 6 two-year olds at a daycare center. Their ages, in months, are 2525 , 2424 , 2828 , 3232 , 2929 , and 3131 . Find the median age.
  3. Brian is teaching a swim class for 66 three-year olds. Their ages, in months, are 38,41,45,36,40,and4238,41,45,36,40,\text{and}42. Find the median age.

    Answer: 40.5 months

  4. Sal recorded the amount he spent for gas each week for the past 88 weeks. The amounts were {$38.65}, {$32.18}, {$40.23}, {$51.50}, {$43.68}, {$30.96}, {$41.37}, and {$44.72}. Find the median amount.
  5. The ages of the eight men in Jerry’s model train club are 52,63,45,51,55,75,60,and5952,63,45,51,55,75,60,\text{and}59. Find the median age.
  6. The number of clients at Miranda’s beauty salon each weekday last week were 18,7,12,16,and2018,7,12,16,\text{and}20. Find the median number of clients.

    Answer: 16 clients

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.
  1. 22 , 55 , 11 , 55 , 22 , 11 , 22 , 33 , 22 , 33 , 11

    Answer: 2

  2. 88 , 55 , 11 , 33 , 77 , 11 , 11 , 77 , 11 , 88 , 77
  3. 1818 , 2222 , 1717 , 2020 , 1919 , 2020 , 2222 , 1919 , 2929 , 1818 , 2323 , 2525 , 2222 , 2424 , 2323 , 2222 , 1818 , 2020 , 2222 , 2020

    Answer: 22

  4. 4242 , 2828 , 3232 , 3535 , 2424 , 3232 , 4848 , 3232 , 3232 , 2424 , 3535 , 2828 , 3030 , 3535 , 4545 , 3232 , 2828 , 3232 , 4242 , 4242 , 3030
  5. The number of children per house on one block: 11 , 44 , 22 , 33 , 33 , 22 , 66 , 22 , 44 , 22 , 00 , 33 , 00.

    Answer: 2 children

  6. The number of movies watched each month last year: 22 , 00 , 33 , 00 , 00 , 88 , 66 , 55 , 00 , 11 , 22 , 33.
  7. The number of units being taken by students in one class: 1212 , 55 , 1111 , 1010 , 1010 , 1111 , 55 , 1111 , 1111 , 1111 , 1010 , 1212 .

    Answer: 11 units

  8. The number of hours of sleep per night for the past two weeks: 88 , 55 , 77 , 88 , 88 ,
  9. 66 , 66 , 66 , 66 , 99 , 77 , 88 , 88 , 88 .
  10. 66 , 44 , 4,54,5 , 6,66,6 , 44 , 44 , 44 , 33 , 55
  11. The number of siblings of a group of students: 22 , 00 , 33 , 22 , 44 , 11 , 66 , 55 , 44 , 11 , 22 , 33

    Answer: 2

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)
  1. Josue is in a book club with 2020 members. One member is chosen at random each month to select the next month’s book. Find the probability that Josue will be chosen next month.

    Answer: 120,0.05\Large\frac{1}{20}\normalsize,0.05

  2. Jessica is one of eight kindergarten teachers at Mandela Elementary School. One of the kindergarten teachers will be selected at random to attend a summer workshop. Find the probability that Jessica will be selected.
  3. There are 2424 people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth.

    Answer: 124,0.04160.042\Large\frac{1}{24}\normalsize,0.041\stackrel{-}{6}\approx 0.042

  4. Monica has two strawberry yogurts and six banana yogurts in her refrigerator. She will choose one yogurt at random to take to work. Find the probability Monica will choose a strawberry yogurt.
  5. Michel has four rock CDs and six country CDs in his car. He will pick one CD to play on his way to work. Find the probability Michel will pick a rock CD.

    Answer: 410,0.4\Large\frac{4}{10}\normalsize,0.4

  6. Noah is planning his summer camping trip. He can’t decide among six campgrounds at the beach and twelve campgrounds in the mountains, so he will choose one campground at random. Find the probability that Noah will choose a campground at the beach.
  7. Donovan is considering transferring to a 4-year college\text{4-year college}. He is considering 1010 out-of state colleges and 44 colleges in his state. He will choose one college at random to visit during spring break. Find the probability that Donovan will choose an out-of-state college.

    Answer: 1014,0.7142850.714\Large\frac{10}{14}\normalsize,0.\stackrel{\text{---}}{714285}\approx 0.714

  8. There are 258,890,850258,890,850 number combinations possible in the Mega Millions lottery. One winning jackpot ticket will be chosen at random. Brent chooses his favorite number combination and buys one ticket. Find the probability Brent will win the jackpot. Round the decimal to the first digit that is not zero, then write the name of the decimal.
  9. The Sustainability Club sells 200200 tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.
  10. Luc has to read 33 novels and 1212 short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

Everyday Math

  1. Joaquin gets paid every Friday. His paychecks for the past 88 Fridays were {$315}, {$236.25}, {$236.25}, {$236.25}, {$315}, {$315}, {$236.25}, {$393.75}. Find the ⓐ mean, ⓑ median, and ⓒ mode.

    Answer: ⓐ $285.47 ⓑ $275.63 ⓒ $236.25

  2. The cash register receipts each day last week at a coffee shop were {$1,845}, {$1,520}, {$1,438}, {$1,682}, {$1,850}, {$2,721}, {$2,539}. Find the ⓐ mean, ⓑ median, and ⓒ mode.

Writing Exercises

Explain in your own words the difference between the mean, median, and mode of a set of numbers. [practice-area rows="4"][/practice-area] Make an example of probability that relates to your life. Write your answer as a fraction and explain what the numerator and denominator represent. [practice-area rows="4"][/practice-area]
 

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.
  1. 2020 to 3636

    Answer: 59\Large\frac{5}{9}

  2. 2020 to 3232
  3. 4242 to 4848

    Answer: 78\Large\frac{7}{8}

  4. 4545 to 5454
  5. 4949 to 2121

    Answer: 73\Large\frac{7}{3}

  6. 5656 to 1616
  7. 8484 to 3636

    Answer: 73\Large\frac{7}{3}

  8. 6.46.4 to 0.80.8
  9. 0.560.56 to 2.82.8

    Answer: 15\Large\frac{1}{5}

  10. 1.261.26 to 4.24.2
  11. 1231\Large\frac{2}{3} to 2562\Large\frac{5}{6}

    Answer: 1017\Large\frac{10}{17}

  12. 1341\Large\frac{3}{4} to 2582\Large\frac{5}{8}
  13. 4164\Large\frac{1}{6} to 3133\Large\frac{1}{3}

    Answer: 54\Large\frac{5}{4}

  14. 5355\Large\frac{3}{5} to 3353\Large\frac{3}{5}
  15. {$18} to {$63}

    Answer: 27\Large\frac{2}{7}

  16. {$16} to {$72}
  17. {$1.21} to {$0.44}

    Answer: 114\Large\frac{11}{4}

  18. {$1.38} to {$0.69}
  19. 2828 ounces to 8484 ounces

    Answer: 13\Large\frac{1}{3}

  20. 3232 ounces to 128128 ounces
  21. 1212 feet to 4646 feet

    Answer: 623\Large\frac{6}{23}

  22. 1515 feet to 5757 feet
  23. 246246 milligrams to 4545 milligrams

    Answer: 8215\Large\frac{82}{15}

  24. 304304 milligrams to 4848 milligrams
  25. total cholesterol of 175175 to HDL cholesterol of 4545

    Answer: 359\Large\frac{35}{9}

  26. total cholesterol of 215215 to HDL cholesterol of 5555
  27. 2727 inches to 11 foot

    Answer: 94\Large\frac{9}{4}

  28. 2828 inches to 11 foot
  29. 2828 to 40405656 to 3232

    Answer: 74\Large\frac{7}{4}

  30. 3.53.5 to 0.50.5
  31. 1.21.2 to 1.81.8

    Answer: 23\Large\frac{2}{3}

  32. 134to1581\Large\frac{3}{4}\normalsize\text{to}1\Large\frac{5}{8}
  33. 213to5142\Large\frac{1}{3}\normalsize\text{to}5\Large\frac{1}{4}

    Answer: 49\Large\frac{4}{9}

  34. 6464 ounces to 3030 ounces
  35. 2828 inches to 33 feet

    Answer: 79\Large\frac{7}{9}

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.
  1. 140140 calories per 1212 ounces

    Answer: 35 calories3 ounces\Large\frac{\text{35 calories}}{\text{3 ounces}}

  2. 180180 calories per 1616 ounces
  3. 8.28.2 pounds per 33 square inches

    Answer: 41 lbs15 sq. in.\Large\frac{\text{41 lbs}}{\text{15 sq. in}.}

  4. 9.59.5 pounds per 44 square inches
  5. 488488 miles in 77 hours

    Answer: 488 miles7 hours\Large\frac{\text{488 miles}}{\text{7 hours}}

  6. 527527 miles in 99 hours
  7. {$595} for 4040 hours

    Answer: \Large\frac{{$119}}{{8 hours}}

  8. {$798} for 4040 hours
  9. 180180 calories per 88 ounces
  10. 9090 pounds per 7.57.5 square inches

    Answer: 90pounds7.5square inches\Large\frac{90\text{pounds}}{7.5\text{square inches}}

  11. 126126 miles in 44 hours
  12. {$612.50} for 3535 hours

    Answer: \Large\frac{$612.50}{35\text{hours}}

Find Unit Rates

Exercise 1

In the following exercises, find the unit rate. Round to two decimal places, if necessary.
    1. 140140 calories per 1212 ounces

      Answer: 11.67 calories/ounce

    2. 180180 calories per 1616 ounces
    3. 8.28.2 pounds per 33 square inches

      Answer: 2.73 lbs./sq. in.

    4. 9.59.5 pounds per 44 square inches
    5. 488488 miles in 77 hours

      Answer: 69.71 mph

    6. 527527 miles in 99 hours
    7. {$595} for 4040 hours

      Answer: $14.88/hour

    8. {$798} for 4040 hours
    9. 576576 miles on 1818 gallons of gas

      Answer: 32 mpg

    10. 435435 miles on 1515 gallons of gas
    11. 4343 pounds in 1616 weeks

      Answer: 2.69 lbs./week

    12. 5757 pounds in 2424 weeks
    13. 4646 beats in 0.50.5 minute

      Answer: 92 beats/minute

    14. 5454 beats in 0.50.5 minute
    15. 180180 calories per 88 ounces
    16. 9090 pounds per 7.57.5 square inches

      Answer: 12 pounds/sq.in.

    17. 126126 miles in 44 hours
    18. {$612.50} for 3535 hours

      Answer: $17.50/hour

Exercise 2

    1. The bindery at a printing plant assembles 96,00096,000 magazines in 1212 hours. How many magazines are assembled in one hour?

      Answer: 8,000

    2. The pressroom at a printing plant prints 540,000540,000 sections in 1212 hours. How many sections are printed per hour?

Find Unit Price

Exercise 1

In the following exercises, find the unit price. Round to the nearest cent.
    1. Soap bars at 88 for {$8.69}

      Answer: $1.09/bar

    2. Soap bars at 44 for {$3.39}
    3. Women’s sports socks at 66 pairs for {$7.99}

      Answer: $1.33/pair

    4. Men’s dress socks at 33 pairs for {$8.49}
    5. Snack packs of cookies at 1212 for {$5.79}

      Answer: $0.48/pack

    6. Granola bars at 55 for {$3.69}
    7. CD-RW discs at 2525 for {$14.99}

      Answer: $0.60/disc

    8. CDs at 5050 for {$4.49}
    9. t-shirts: 33 for {$8.97}
    10. Highlighters: 66 for {$2.52}

      Answer: $0.42

    11. An office supply store sells a box of pens for {$11}. The box contains 1212 pens. How much does each pen cost?
    12. Anna bought a pack of 88 kitchen towels for {$13.20}. How much did each towel cost? Round to the nearest cent if necessary.

      Answer: $1.65

Exercise 2

    1. The grocery store has a special on macaroni and cheese. The price is {$3.87} for 33 boxes. How much does each box cost?

      Answer: $1.29/box

    2. The pet store has a special on cat food. The price is {$4.32} for 1212 cans. How much does each can cost?

Exercise 3

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.
    1. Mouthwash, 50.7ounce{50.7-ounce} size for {$6.99} or 33.8ounce{33.8-ounce} size for {$4.79}

      Answer: The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy.

    2. Toothpaste, 66 ounce size for {$3.19} or 7.8ounce7.8-ounce size for {$5.19}
    3. Breakfast cereal, 1818 ounces for {$3.99} or 1414 ounces for {$3.29}

      Answer: The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy.

    4. Breakfast Cereal, 10.710.7 ounces for {$2.69} or 14.814.8 ounces for {$3.69}
    5. Ketchup, 40ounce{40-ounce} regular bottle for {$2.99} or 64ounce{64-ounce} squeeze bottle for {$4.39}

      Answer: The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.

    6. Mayonnaise 15ounce{15-ounce} regular bottle for {$3.49} or 22ounce{22-ounce} squeeze bottle for {$4.99}
    7. Cheese {$6.49} for 11 lb. block or {$3.39} for 12\Large\frac{1}{2} lb. block

      Answer: The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.

    8. Candy {$10.99} for a 11 lb. bag or {$2.89} for 14\Large\frac{1}{4} lb. of loose candy
    9. Shampoo: 1212 ounces for {$4.29} or 2222 ounces for {$7.29}?
    10. Vitamins: 6060 tablets for {$6.49} or 100100 for {$11.99}?

      Answer: $0.11, $0.12; 60 tablets for $6.49

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.
    1. 793793 miles per pp hours

      Answer: 793 milesphours\Large\frac{\text{793 miles}}{p \text{hours}}

    2. 7878 feet per rr seconds
    3. {$3} for 0.50.5 lbs.

      Answer: \Large\frac{{$3}}{{0.5 lbs}.}

    4. jj beats in 0.50.5 minutes
    5. 105105 calories in xx ounces

      Answer: 105 caloriesxounces\Large\frac{\text{105 calories}} {x \text {ounces}}

    6. 400400 minutes for mm dollars
    7. the ratio of yy and 5x5x

      Answer: y5x\Large\frac{y}{5x}

    8. the ratio of 12x12x and yy
    9. 535535 miles per hhoursh\text{hours}
    10. aa adults to 4545 children

      Answer: aadults45children\Large\frac{a\text{adults}}{45\text{children}}

    11. the ratio of 4y4y and the difference of xx and 1010
    12. the ratio of 1919 and the sum of 33 and nn

      Answer: 193+n\Large\frac{19}{3+n}

Everyday Math

Everyday math

  1. One elementary school in Ohio has 684684 students and 4545 teachers. Write the student-to-teacher ratio as a unit rate.

    Answer: 15.2 students per teacher

  2. The average American produces about 1,6001,600 pounds of paper trash per year (365 days). How many pounds of paper trash does the average American produce each day? (Round to the nearest tenth of a pound.)
  3. A popular fast food burger weighs 7.57.5 ounces and contains 540540 calories, 2929 grams of fat, 4343 grams of carbohydrates, and 2525 grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce. Round to two decimal places.

    Answer: ⓐ 72 calories/ounce ⓑ 3.87 grams of fat/ounce ⓒ 5.73 grams carbs/once ⓓ 3.33 grams protein/ounce

  4. A 16ounce16-ounce chocolate mocha coffee with whipped cream contains 470470 calories, 1818 grams of fat, 6363 grams of carbohydrates, and 1515 grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce.
 

Writing Exercises

  1. Would you prefer the ratio of your income to your friend’s income to be 3/1\text{3/1} or 1/3?1/3? Explain your reasoning. Answers will vary.
  2. The parking lot at the airport charges {$0.75} for every 1515 minutes. ⓐ How much does it cost to park for 11 hour? ⓑ Explain how you got your answer to part ⓐ. Was your reasoning based on the unit cost or did you use another method?
  3. Kathryn ate a 4ounce4-ounce cup of frozen yogurt and then went for a swim. The frozen yogurt had 115115 calories. Swimming burns 422422 calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning. Answers will vary.
  4. Mollie had a 16ounce16-ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110110 calories. If Mollie walks for one hour, she burns 246246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.
  Simplify Expressions with Square Roots In the following exercises, simplify.
    1. 36\sqrt{36}

      Answer: 6

    2. 4\sqrt{4}
    3. 64\sqrt{64}

      Answer: 8

    4. 144\sqrt{144}
    5. 4-\sqrt{4}

      Answer: −2

    6. 100-\sqrt{100}
    7. 1-\sqrt{1}

      Answer: −1

    8. 121-\sqrt{121}
    9. 121\sqrt{-121}

      Answer: not a real number

    10. 36\sqrt{-36}
    11. 9\sqrt{-9}

      Answer: not a real number

    12. 49\sqrt{-49}
    13. 9+16\sqrt{9+16}

      Answer: 5

    14. 25+144\sqrt{25+144}
    15. 9+16\sqrt{9}+\sqrt{16}

      Answer: 7

    16. 25+144\sqrt{25}+\sqrt{144}
    17. 64\sqrt{64}
    18. 144\sqrt{144}

      Answer: 12

    19. 25-\sqrt{25}
    20. 81-\sqrt{81}

      Answer: −9

    21. 9\sqrt{-9}
    22. 36\sqrt{-36}

      Answer: not a real number

    23. 64+225\sqrt{64}+\sqrt{225}
    24. 64+225\sqrt{64+225}

      Answer: 17

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.
    1. 70\sqrt{70}

      Answer: 8<70<98<\sqrt{70}<9

    2. 55\sqrt{55}
    3. 200\sqrt{200}

      Answer: 14<200<1514<\sqrt{200}<15

    4. 172\sqrt{172}
    5. 28\sqrt{28}
    6. 155\sqrt{155}

      Answer: 12<155<1312<\sqrt{155}<13

Approximate Square Roots with a Calculator

In the following exercises, use a calculator to approximate each square root and round to two decimal places.
    1. 19\sqrt{19}

      Answer: 4.36

    2. 21\sqrt{21}
    3. 53\sqrt{53}

      Answer: 7.28

    4. 47\sqrt{47}
    5. 15\sqrt{15}
    6. 57\sqrt{57}

      Answer: 7.55

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)
    1. y2\sqrt{{y}^{2}}

      Answer: y

    2. b2\sqrt{{b}^{2}}
    3. 49x2\sqrt{49{x}^{2}}

      Answer: 7x

    4. 100y2\sqrt{100{y}^{2}}
    5. 64a2-\sqrt{64{a}^{2}}

      Answer: −8a

    6. 25x2-\sqrt{25{x}^{2}}
    7. 144x2y2\sqrt{144{x}^{2}{y}^{2}}

      Answer: 12xy

    8. 196a2b2\sqrt{196{a}^{2}{b}^{2}}
    9. q2\sqrt{{q}^{2}}
    10. 64b2\sqrt{64{b}^{2}}

      Answer: 8b

    11. 121a2-\sqrt{121{a}^{2}}
    12. 225m2n2\sqrt{225{m}^{2}{n}^{2}}

      Answer: 15mn

    13. 100q2-\sqrt{100{q}^{2}}
    14. 49y2\sqrt{49{y}^{2}}

      Answer: 7y

    15. 4a2b2\sqrt{4{a}^{2}{b}^{2}}
    16. 121c2d2\sqrt{121{c}^{2}{d}^{2}}

      Answer: 11cd

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place. Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 7575 square feet. How long can a side of his garden be?
      1. Answer: 8.7 feet

    Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130130 square feet. How long can a side of his patio be? Gravity An airplane dropped a flare from a height of 1,0241,024 feet above a lake. How many seconds did it take for the flare to reach the water?
        1. Answer: 8 seconds

      Gravity A hiker dropped a granola bar from a lookout spot 576576 feet above a valley. How long did it take the granola bar to reach the valley floor? Gravity A hang glider dropped his cell phone from a height of 350350 feet. How many seconds did it take for the cell phone to reach the ground? Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, 4,0004,000 feet above the Colorado River. How many seconds did it take for the hammer to reach the river?
          1. Answer: 15.8 seconds

        Accident investigation The skid marks from a car involved in an accident measured 5454 feet. What was the speed of the car before the brakes were applied? Accident investigation The skid marks from a car involved in an accident measured 216216 feet. What was the speed of the car before the brakes were applied?
            1. Answer: 72 mph

          Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175175 feet. What was the speed of the vehicle before the brakes were applied? Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117117 feet. What was the speed of the vehicle before the brakes were applied?
              1. Answer: 53.0 mph

            1. Everyday Math

              1. Decorating Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy 625625 square centimeters of the designer tiles. How long can a side of the accent be?Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2,0252,025 tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be?

                Answer: 45 inches

              Writing exercises

              • Why is there no real number equal to 64?\sqrt{-64}?
              • What is the difference between 92{9}^{2} and 9?\sqrt{9}? Answers will vary. 92 reads: "nine squared" and means nine times itself. The expression 9\sqrt{9} reads: "the square root of nine" which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.
                 

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