WORD PROBLEMS ON SQUARE ROOTS

Example 1 :

You have a square blanket that has an area of 1600 square inches. What is the length of 1 side of the blanket ?

Solution :

Given,

Area of a square blanket  =  1600 sq.inches

Formula for area of a square,

Area  =  s²

1600  =  s²

s  =  √1600

s  =  400 inches

So, the length of 1 side of the blanket is 400 inches.

Example 2 :

A square coffee table has an area of 196 square inches. What is the length of one side of the coffee table ?

Solution :

Given,

Area of a square coffee table  =  196 sq.inches

Formula for area of a square,

Area  =  s²

196  =  s²

s  =  √196

s  =  14 inches

So, the length of one side of the coffee table is 14 inches.

Example 3 :

You have a square flower garden that has an area of 400 square yards. What is the length of one side of the garden ?

Solution :

Given, 

Area of square flower garden  =  400 square yards

Area  =  s²

400  =  s²

s  =  √400

s  =  20 yards

So, the length of one side of the garden is 20 yards.

Example 4 :

A square desktop has an area of 324 square inches. What is the length of one side of the desktop ?

Solution :

Given, 

Area of square desktop  =  324 square inches

Area  =  s²

324  =  s²

s  =  √324

s  =  18 inches

So, the length of one side of the desktop is 18 inches.

Example 5 :

You want to carpet a square room that has an area of 144 square feet. What is the length of one side of the room ? 

Solution :

Given, 

Area of square room  =  144 square feet

Area  =  s²

144  =  s²

s  =  √144

s  =  12 feet

So, the length of one side of the room is 12 feet.

Example 6 :

You are going to decorate one wall of your bedroom  by putting border along the top. The wall is a square wall with an area of 256 square feet. What is the length of  border you need for the top of this on wall ?

Solution :

Given, 

Area of square wall  =  256 square feet

Area  =  s²

256  =  s²

s  =  √256

s  =  16 feet

So, the length of border on top of wall is 16 feet.

Example 7 :

To the nearest tenth, what is the square root of 33 ?

Solution :

The square root of 33  =  5.744

Since the hundredth digit in 5.744 is less than 5, we can round answer as 5.7

So, the square root of 33 is 5.7

Example 8 :

The area of a square tile is 50 square centimeters. To the nearest tenth of a centimeter, how long is one side of this tile ?

Solution :

Given,

Area of square tile  =  50 square centimeters

Area  =  s²

50  =  s²

s  =  √50

s  =  7.07 centimeter

Since the hundredth digit in 7.07 is greater than 5, we can add 1 with the tenth digit. Then we approximate the answer as 7.1

s  =  7.1 centimeter

So, the length of one side of tile is 7.1 cm.

Example 9 :

Jason's square bedroom has an area of 90 square feet. The length of one side of his room is between what two whole numbers ?

Solution :

Given,

Area of square bedroom  =  90 square feet

Area  =  s²

90  =  s²

s  =  √90

s  =  9.48 feet

Then, the square root of 90 is between two whole numbers are 9 and 10.

So, the length of one side of room is between 9 and 10.

Example 10 :

Grandma's square garden has an area of 90 square feet. The length of one side of her garden would be between what two whole numbers ? What is the length of this side to the nearest tenth of a foot ?

Solution :

Given,

Area of square garden  =  90 square feet

Area  =  s²

90  =  s²

s  =  √90

s  =  9.48 feet

Then, the square root of 90 is between two whole numbers are 9 and 10.

So, the length of one side of garden is between 9 and 10.

Since the hundredth digit in 9.48 is greater than 5, we can add 1 by the tenth digit. Then we can approximate the answer as 9.5

s  =  9.5 feet

So, the length of side to the nearest tenth is 9.5 feet.

Example 11 :

The least perfect square number divisible by 3, 4, 5, 6,  and 8 is :

a)  900      b)  1200      c)  2500      d)  3600

Solution :

Option a :

900 = 2 x 2 x 5 x 5 x 3 x 3

= (2 x 5 x 3)²

From the above factors it is clear that, 900 is the factor of 2, 3, 5, 6, 15, 4, 25, 9 and so on. It is clear that 8 is not a factor of 900. Then option a is not correct.

Option b :

1200 = 2⁴ x 3 x 5²

Here it is clear that 2, 3, 5, 6, 4, 8, 16, 25 an so on are the factors. But 1200 is not a perfect square.

Option c :

2500 is perfect square but it may not be the multiple of 8. 

Option d :

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

= 2⁴ x 3² x 5²

2, 3, 4, 6, 9, 8, 16, 25, and so on. It is perfect square also. So, option d is correct.

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