# SQUARE AND CUBE ROOTS OF RATIONAL NUMBERS WORKSHEET

## About "Square and cube roots of rational numbers worksheet"

Square and cube roots of rational numbers worksheet :

Here we are going to see some practice questions on finding square and cube roots of rational numbers.

## Square and cube roots of rational numbers worksheet - Practice questions

(1)  Find the root of the following rational number

√64

(2)  Find the root of the following rational number

√(1/4)

(3)  Find the root of the following rational number

∛(8/125)

(4)  Find the root of the following rational number

∛(1/64)

(5)  Find the root of the following rational number

(36/81)

(6)  Find the root of the following rational number

(81/100)

(7)  Find the root of the following rational number

∛(125/216)

(8)  Find the root of the following rational number

∛(125/27)

## Square and cube roots of rational numbers worksheet - Solution

 Question 1 :Find the root of the following rational number√64Solution :Step 1 :Index of the given rational number is 2.  =  √64Step 2 :Spliting the number as much as possible.  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)Step 3 :Since the index is 2, we have to take one common number for every two same terms.  =  2 ⋅ 2 ⋅ 2   =  8

Question 2 :

Find the root of the following rational number

√(1/4)

Solution :

Step 1 :

Index of the given rational number is 2.

=  √(1/4)

Step 2 :

Spliting the number as much as possible.

=  √(1/2) ⋅ (1/2)

Step 3 :

Since the index is 2, we have to take one common number for every two same terms.

=  1/2

Let us look into the solution of next problem on "Square and cube roots of rational numbers worksheet".

Question 3 :

Find the root of the following rational number

∛(8/125)

Solution :

Step 1 :

Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.

=  ∛8/∛125

Step 2 :

Spliting the number as much as possible.

=  ∛(2 ⋅ 2 ⋅ 2)/∛(5 ⋅ 5 ⋅ 5)

Step 3 :

Since the index is 3, we have to take one common number for every three same terms.

=  2/5

Question 4 :

Find the root of the following rational number

∛(1/64)

Solution :

Step 1 :

Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.

=  ∛1/∛64

Step 2 :

Spliting the number as much as possible.

=  ∛(1 ⋅ 1 ⋅ 1)/∛(4 ⋅ 4 ⋅ 4)

Step 3 :

Since the index is 3, we have to take one common number for every three same terms.

=  1/4

Question 5 :

Find the root of the following rational number

(36/81)

Solution :

Step 1 :

Index of the given rational number is 2.Now we need to take separate square roots for both numerator and denominator.

=  √(36/81)

=  √36/81

Step 2 :

Spliting the number as much as possible.

=  √(2⋅2⋅3⋅3)/√(3⋅3⋅3⋅3)

Step 3 :

Since the index is 2, we have to take one common number for every two same terms.

=  (2⋅3)/(3⋅3)

=  2/3

Question 6 :

Find the root of the following rational number

(81/100)

Solution :

Step 1 :

Index of the given rational number is 2.Now we need to take separate square roots for both numerator and denominator.

=  √(81/100)

=  √81/√100

Step 2 :

Spliting the number as much as possible.

=  √(3⋅3⋅3⋅3)/√(10⋅10)

Step 3 :

Since the index is 2, we have to take one common number for every two same terms.

=  (2⋅3)/(3⋅3)

=  2/3

Question 7 :

Find the root of the following rational number

∛(125/216)

Solution :

Step 1 :

Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.

=  ∛125/∛216

Step 2 :

Spliting the number as much as possible.

=  ∛(5 ⋅ 5 ⋅ 5)/∛(6 ⋅ 6 ⋅ 6)

Step 3 :

Since the index is 3, we have to take one common number for every three same terms.

=  5/6

Question 8 :

Find the root of the following rational number

∛(125/27)

Solution :

Step 1 :

Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.

=  ∛125/∛27

Step 2 :

Spliting the number as much as possible.

=  ∛(5 ⋅ 5 ⋅ 5)/∛(3 ⋅ 3 ⋅ 3)

Step 3 :

Since the index is 3, we have to take one common number for every three same terms.

=  5/3

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