**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.

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.

**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.

After having gone through the stuff given above, we hope that the students would have understood "Finding square roots and cube roots worksheet".

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