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

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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.

#### Questions & Answers

the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0
What is observation
I'm confused by the question. Can you describe or explain the math question it pertains to?
Melissa
there is no math to it because all you use is your vision or gaze to the sorrounding areas
Cesarp
Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him$10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?
5 times max
Anton
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 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
35 min
Debra
Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs $1.50 per square foot, but also wants to use an accent tile that costs$9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be $3 per square foot? Parker Reply what you wanna get Cesar 800 sq. ft @$1.50 & 200 sq. ft @ $9.00 Marco Geneva treated her parents to dinner at their favorite restaurant. The bill was$74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be?
74.25 × .16 then get the total and that will be your tip
David
$74.25 x 0.16 =$11.88 total bill: $74.25 +$11.88 = $86.13 ericka yes and tip 16% will be$11.88
David
what is the shorter way to do it
Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup? Alexandra Reply Uno de los ángulos suplementario es 4° más que 1/3 del otro ángulo encuentra las medidas de cada uno de los angulos Enith Reply June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold? Alexandra Reply I hope this is correct, x=cooler 1 5x=cooler 2 x + 5x = 48 6x=48 ×=8 gallons 5×=40 gallons ericka Priam has pennies and dimes in a cup holder in his car. The total value of the coins is$4.21 . The number of dimes is three less than four times the number of pennies. How many pennies and how many dimes are in the cup?
Arnold invested $64,000 some at 5.5% interest and the rest at 9% interest how much did he invest at each rate if he received$4500 in interest in one year
List five positive thoughts you can say to yourself that will help youapproachwordproblemswith a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.
Avery and Caden have saved \$27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?
324.00
Irene
1.2% of 27.000
Irene
i did 2.4%-7.2% i got 1.2%
Irene
I have 6% of 27000 = 1620 so we need to solve 2.4x +7.2y =1620
Catherine
I think Catherine is on the right track. Solve for x and y.
Scott
next bit : x=(1620-7.2y)/2.4 y=(1620-2.4x)/7.2 I think we can then put the expression on the right hand side of the "x=" into the second equation. 2.4x in the second equation can be rewritten as 2.4(rhs of first equation) I write this out tidy and get back to you...
Catherine
Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that enclose his rectangular front yard. The length is five feet less than five times the width. Find the length and width of the fencing. By Gerr Zen      By Rhodes By  By