WORD PROBLEMS ON SQUARE ROOTS

Problem 1 :

Landscaping Read wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. How long can a side of his garden be?

Solution :

Let ‘s’ be the side length of the square.

Area of the square = s²

Area of the square garden = 75 square feet

75 = s²

To find the value of s, take square roots on both sides.

s = √75

s = 8.66

So, the side length of the garden is 8.66 feet.

Problem 2 :

Landscaping Read wants to have a square garden plot in his backyard. He has enough compost to cover an area of 130 square feet. How long can a side of his garden be?

Solution :

Let ‘s’ be the side length of the square.

Area of the square = s²

Area of the square garden = 130 square feet

130 = s²

To find the value of s, take square roots on both sides.

s = √130

s = 11.402

So, the side length of the garden is 11.402.

Problem 3 :

Decorating Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy 625 square centimeters of designer tiles. How long can a side of the accent be? 

Solution :

Let A be a square centimeters = 625 

Area of the square = s²

 625 = s²

s = √625

s = 25

So, the side length of the accent is 25.

Problem 4 :

Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2,025 tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be? 

Solution :

Let A be a square with an area = 2,025

Area of the square = s²

s = √2025

s = 45

So, the side length of the mosaic is 45.

Problem 5 :

Amber wants to put carpet on the floor of her bedroom. The floor is a square with an area of 182.25 square feet. How long should the piece of carpet be on each side?

Solution :

Area of a square of the floor = 182.25 square feet.

Let s be the side of the piece of carpet.

Area of the square = s²

182.25 = s²

s = √(182.25)

s = 13.5 feet

Problem 6 :

A square has a side length of 3x and an area of 324 in². What is the value of x ?

Solution :

Area of  square (A) = 324 in²

Length of the side (s) = 3x

Area of the square = s²

 324 = (3x)²

324 = 9x²

(324)/9 = x²

36 = x²

x = √36

x = 6

So, the value of x is 6.

Problem 7 :

The area of a square is 144 cm². What is the length of one side?

Solution :

Area of a square = 144 cm²

Length of one side = ?

Area of the square = s²

144 = s²

s = √144

s = 12 cm

So, the length of one side is 12 cm.

Problem 8 :

The area of a square is 289 m². What is the perimeter of the square?

Solution :

Area of a square = 289 m²

Let a be the side.

Area of the square = a²

289 = a²

a = √289

a = 17

To find the perimeter of the square,

Perimeter = 4a

P = 4(17)

P = 68