# 9.6 Solve equations with square roots  (Page 3/6)

 Page 3 / 6

We used the formula $A=L·W$ to find the area of a rectangle with length L and width W . A square is a rectangle in which the length and width are equal. If we let s be the length of a side of a square, the area of the square is ${s}^{2}$ .

The formula $A={s}^{2}$ gives us the area of a square if we know the length of a side. What if we want to find the length of a side for a given area? Then we need to solve the equation for s .

$\begin{array}{cccc}& & & \phantom{\rule{0.5em}{0ex}}A={s}^{2}\hfill \\ \text{Take the square root of both sides.}\hfill & & & \sqrt{A}=\sqrt{{s}^{2}}\hfill \\ \text{Simplify.}\hfill & & & \sqrt{A}=s\hfill \end{array}$

We can use the formula $s=\sqrt{A}$ to find the length of a side of a square for a given area.

## Area of a square

We will show an example of this in the next example.

Mike and Lychelle want to make a square patio. They have enough concrete to pave an area of 200 square feet. Use the formula $s=\sqrt{A}$ to find the length of each side of the patio. Round your answer to the nearest tenth of a foot.

## Solution

 Step 1. Read the problem. Draw a figure and label it with the given information. A = 200 square feet Step 2. Identify what you are looking for. The length of a side of the square patio. Step 3. Name what you are looking for by choosing a variable to represent it. Let s = the length of a side. Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute the given information. Step 5. Solve the equation using good algebra techniques. Round to one decimal place. Step 6. Check the answer in the problem and make sure it makes sense. This is close enough because we rounded the square root. Is a patio with side 14.1 feet reasonable? Yes. Step 7. Answer the question with a complete sentence. Each side of the patio should be 14.1 feet.

Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of 370 square feet. Use the formula $s=\sqrt{A}$ to find the length of each side of her lawn. Round your answer to the nearest tenth of a foot.

$19.2\phantom{\rule{0.2em}{0ex}}\text{yards}$

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. Use the formula $s=\sqrt{A}$ to find the length of each side of his mosaic. Round your answer to the nearest tenth of a foot.

$52.0\phantom{\rule{0.2em}{0ex}}\text{cm}$

Another application of square roots has to do with gravity.

## 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,

$t=\frac{\sqrt{h}}{4}$

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 substituting $h=64$ into the formula.

 Take the square root of 64. Simplify the fraction.

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. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the sunglasses to reach the river.

## Solution

 Step 1. Read the problem. Step 2. Identify what you are looking for. The time it takes for the sunglasses to reach the river. Step 3. Name what you are looking for by choosing a variable to represent it. Let t = time. Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information. Step 5. Solve the equation using good algebra techniques. Step 6. Check the answer in the problem and make sure it makes sense. $5=5✓\phantom{\rule{4.5em}{0ex}}$ Does 5 seconds seem reasonable? Yes. Step 7. Answer the question with a complete sentence. It will take 5 seconds for the sunglasses to hit the water.

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?
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.
p-2/3=5/6 how do I solve it with explanation pls
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
yes
James
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?
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
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?
integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy
He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least \$2,400?
at least 20
Ayla
what are the steps?
Alicia
6.4 jobs
Grahame
32
Grahame
1600+2400= total amount with expenses. 4000/125= number of jobs needed to make that min profit of 2400. answer is 32
Orlando
He must work 32 jobs to make a profit
POP
32
Cindy
what is algebra
repeated addition and subtraction of the order of operations. i love algebra I'm obsessed.
Shemiah
hi
Krekar
Eric here. I'm a parent. 53 years old. I have never taken algebra. I want to learn.
Eric
I am 63 and never learned algebra
Cindy
One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?
they are 92 candies in the bag
POP
92
Cindy