SOLVING EQUATIONS WITH SQUARE ROOTS WORKSHEET

Solve the following equations for x :

Problem 1 :

5√2 = √x Solution

Problem 2 :

3√x = √45 Solution

Problem 3 :

2√2 = √4x Solution

Problem 4 :

√(x + 1) = 6

what value of x satisfies the equation above ?

(a) 5 (b) 6 (c) 35 (d) 36

Solution

Problem 5 :

(x - 12) = √(x + 44)

What are all possible solution to the given equation ?

(a) 5 (b) 20 (c) -5 and 20 (d) 5 and 20

Solution

Problem 6 :

x + 3√x = 28 Solution

Problem 7 :

Solve for x, 3/x = √0.09

Problem 8 :

A Shell station stores its gasoline in underground tanks that are right circular cylinders lying on their sides.See the illustration. The volume V of gasoline in the tank (in gallons) is given by the formula

V = 40h²√(96/h) - 0.608

where h is the height of the gasoline (in inches) as measured on a depth stick.

(a) If h = 12 inches, how many gallons of gasoline are in the tank?

(b) If h = 1 inch, how many gallons of gasoline are in the tank?

Problem 9 :

Solve √(3 - 2√x)) = √x

Problem 10 :

If c = 3√5 and 5c = √5z, what is the value of z ?

Problem 11 :

In the equation y - √(4x² + 28) = 0, x > 0 and y = 8. What is the value of x ?

Example 12 :

If k = 1, which of the following is the solution set for x - 7 = √(x - k) ?

1) x = 50

2) x = 5

3) x = 2

4) x = 35

Word Problems on Square Roots

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

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

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

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

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

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

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

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

SOLVING EQUATIONS WITH SQUARE ROOTS WORKSHEET

Word Problems on Square Roots

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