# FINDING SQUARE ROOTS AND CUBE ROOTS WORKSHEET

## About "Finding square roots and cube roots worksheet"

Finding square roots and cube roots worksheet :

Worksheet on finding square roots and cube roots is much useful to the students who would like to practice problems involving square roots and cube roots.

## Finding square roots and cube roots worksheet - Problems

1.  Solve the equation x²  =  121 for "x".

2.  Solve the equation x²  =  16/169 for "x".

3.  Solve the equation x³  =  729 for "x".

4.  Solve the equation x³  =  8/125 for "x".

5. Can you solve the equation x² =  27 and get an irrational number as solution ? Explain.

## Finding square roots and cube roots worksheet - Solution

Problem 1 :

Solve the equation x²  =  121 for "x".

Solution :

x²  =  121

Solve for x by taking the square root of both sides.

x  =  ± √121

Apply the definition of square root.

Think: What numbers squared equal 121 ?

x  =  ± 11

Hence, the solutions are 11 and −11.

Problem 2 :

Solve the equation x²  =  16/169 for "x".

Solution :

x²  =  16/169

Solve for x by taking the square root of both sides.

x  =  ± √(16/169)

Apply the definition of square root.

Think: What numbers squared equal 16/169 ?

x  =  ± 4/13

Hence, the solutions are 4/13 and −4/13.

Problem 3 :

Solve the equation x³  =  729 for "x".

Solution :

x³  =  729

Solve for x by taking the cube root of both sides.

x  =  729

Apply the definition of cube root.

Think: What number cubed equals 729 ?

x  =  9

Hence, the solutions is 9.

Problem 4 :

Solve the equation x³  =  8/125 for "x".

Solution :

x³  =  8/125

Solve for x by taking the cube root of both sides.

x  =  (8/125)

Apply the definition of cube root.

Think: What number cubed equals 8/125 ?

x  =  2/5

Hence, the solutions is 2/5.

Problem 5 :

Can you solve the equation x² =  27 and get a rational number as solution ? Explain.

Solution :

No, we can not get a rational number as a solution.

In the given equation we have "square" for "x".

So, we will be able to get a rational number as solution, only if we have a perfect square on the right side of the equation.

Since we have 27 (not a perfect square) on the right side of the equation, we can not get a rational number as a solution.

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