# 9.6 Solve equations with square roots  (Page 4/6)

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A helicopter dropped a rescue package from a height of 1,296 feet. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

$9\phantom{\rule{0.2em}{0ex}}\text{seconds}$

A window washer dropped a squeegee from a platform 196 feet above the sidewalk Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the squeegee to reach the sidewalk.

$3.5\phantom{\rule{0.2em}{0ex}}\text{seconds}$

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.

## Skid marks and speed of a car

If the length of the skid marks is d feet, then the speed, s , of the car before the brakes were applied can be found by using the formula,

$s=\sqrt{24d}$

After a car accident, the skid marks for one car measured 190 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

## Solution

 Step 1. Read the problem. Step 2. Identify what we are looking for. The speed of a car. Step 3. Name what we are looking for. Let s = the speed. Step 4. Translate into an equation by writing the appropriate formula. Substitute the given information. Step 5. Solve the equation .  Round to 1 decimal place. Step 6. Check the answer in the problem. $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\sqrt{24\left(190\right)}$ $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\phantom{\rule{0.2em}{0ex}}\sqrt{4560}$ $\phantom{\rule{1em}{0ex}}67.5\stackrel{?}{\approx }\phantom{\rule{0.2em}{0ex}}67.5277...$ Is 67.5 mph a reasonable speed? Yes. Step 7. Answer the question with a complete sentence. The speed of the car was approximately 67.5 miles per hour.

An accident investigator measured the skid marks of the car. The length of the skid marks was 76 feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

$42.7\phantom{\rule{0.2em}{0ex}}\text{feet}$

The skid marks of a vehicle involved in an accident were 122 feet long. Use the formula $s=\sqrt{24d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

$54.1\phantom{\rule{0.2em}{0ex}}\text{feet}$

## Key concepts

• To Solve a Radical Equation:
1. Isolate the radical on one side of the equation.
2. Square both sides of the equation.
3. Solve the new equation.
4. Check the answer. Some solutions obtained may not work in the original equation.
• Solving Applications with Formulas
1. Read the problem and make sure all the words and ideas are understood. When appropriate, draw a figure and label it with the given information.
2. Identify what we are looking for.
3. Name what we are looking for by choosing a variable to represent it.
4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem and make sure it makes sense.
7. Answer the question with a complete sentence.
• Area of a Square • Falling Objects
• 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 using the formula $t=\frac{\sqrt{h}}{4}$ .
• Skid Marks and Speed of a Car
• If the length of the skid marks is d feet, then the speed, s , of the car before the brakes were applied can be found by using the formula $s=\sqrt{24d}$ .

## Practice makes perfect

Solve Radical Equations

#### Questions & Answers

find the solution to the following functions, check your solutions by substitution. f(x)=x^2-17x+72
Carlos Reply
Aziza is solving this equation-2(1+x)=4x+10
Sechabe Reply
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
KAJAL Reply
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
Adedamola Reply
please the answer to the example exercise
Patricia Reply
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
Edwin Reply
.473
Angelita
?
Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
DaYoungan Reply
p-2/3=5/6 how do I solve it with explanation pls
Adedamola Reply
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
don't understand answer
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
Adedamola Reply
yes
James
don't understand answer
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have? Rhonda Reply Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 . Gabriel Reply is that a negative 4 or positive 4? Felix y = mx + b Felix if negative -4, then -4=8/9(0) + b Felix -4=b Felix if positive 4, then 4=b Felix then plug in y=8/9x - 4 or y=8/9x+4 Felix Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost$9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost$6.50 per pound to make?
Cherry Reply
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up Makaila Reply$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
Abdulai Reply
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Rafi Reply
hola saben como aser un valor de la expresión
NAILEA

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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