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Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of 370 square feet. To the nearest tenth of a foot, how long can a side of her square lawn be?

19.2 feet

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Sergio wants to make a square mosaic as an inlay for a table he is building. He has enough tile to cover an area of 2704 square centimeters. How long can a side of his mosaic be?

52 centimeters

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Square roots and gravity

Another application of square root s involves gravity . On Earth, if an object is dropped from a height of h feet, the time in seconds it will take to reach the ground is found by evaluating the expression h 4 . For example, if an object is dropped from a height of 64 feet, we can find the time it takes to reach the ground by evaluating 64 4 .

64 4
Take the square root of 64. 8 4
Simplify the fraction. 2

It would take 2 seconds for an object dropped from a height of 64 feet to reach the ground.

Christy dropped her sunglasses from a bridge 400 feet above a river. How many seconds does it take for the sunglasses to reach the river?

Solution

What are you asked to find? The number of seconds it takes for the sunglasses to reach the river
Write a phrase. The time it will take to reach the river
Translate to an expression. h 4
Evaluate h 4 when h = 400 . 400 4
Find the square root of 400. 20 4
Simplify. 5
Write a sentence. It will take 5 seconds for the sunglasses to reach the river.

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A helicopter drops a rescue package from a height of 1296 feet. How many seconds does it take for the package to reach the ground?

9 seconds

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A window washer drops a squeegee from a platform 196 feet above the sidewalk. How many seconds does it take for the squeegee to reach the sidewalk?

3.5 seconds

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Square roots and accident investigations

Police officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes. According to some formulas, if the length of the skid marks is d feet, then the speed of the car can be found by evaluating 24 d .

After a car accident, the skid marks for one car measured 190 feet. To the nearest tenth, what was the speed of the car (in mph) before the brakes were applied?

Solution

What are you asked to find? The speed of the car before the brakes were applied
Write a phrase. The speed of the car
Translate to an expression. 24 d
Evaluate 24 d when d = 190 . 24 · 190
Multiply. 4,560
Use your calculator. 67.527772 ...
Round to tenths. 67.5
Write a sentence. The speed of the car was approximately 67.5 miles per hour.
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An accident investigator measured the skid marks of a car and found their length was 76 feet. To the nearest tenth, what was the speed of the car before the brakes were applied?

42.7 mph

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The skid marks of a vehicle involved in an accident were 122 feet long. To the nearest tenth, how fast had the vehicle been going before the brakes were applied?

54.1 mph

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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