SQUARE AND CUBE ROOTS OF RATIONAL NUMBERS WORKSHEET

Problem 1 : 

Find the square root of 64.

Problem 2 : 

Find the square root of (1/4).

√(1/4)

Problem 3 : 

Find the cube root of (8/125). 

Problem 4 : 

Find the cube root of (1/64). 

Problem 5 : 

Find the square root of (36/81). 

Problem 6 : 

Find the square root (81/100). 

Problem 7 : 

Find the cube root of (125/216). 

Problem 8 : 

Find the cube root of (27/343). 

Problem 1 :

Find the square root of 64.

Solution :

Step 1 :

√64

Decompose the number inside the radical sign into prime factors. 

  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

Step 2 :

Since the index is 2, we have to take one number out of radical sign for every two same numbers multiplied inside the radical sign. 

  =  ⋅ 2 ⋅ 2 

  =  8




Problem 2 :

Find the square root of (1/4). 

Solution : 

Step 1 :

√(1/4)

Distribute the square root to numerator and denominator.

=  √1 / 4

Step 2 :

Decompose 4 into its prime factors. 

=  1 / √(⋅ 2)

Step 3 :

Since the index is 2, we have to take one number out of radical sign for every two same numbers multiplied inside the radical sign. 

  =  1/2

Problem 3 :

Find the cube root of (8/125). 

Solution : 

Step 1 :

3(8/125)

Distribute the cube root to numerator and denominator.

=  33125

Step 2 :

Decompose the number inside the radical sign into prime factors. 

=  3(2 ⋅ 2 ⋅ 2) / 3(5 ⋅ 5 ⋅ 5)

Step 3 :

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign. 

  =  2/5

Problem 4 :

Find the cube root of (1/64). 

Solution : 

Step 1 :

3(1/64)

Distribute the cube root to numerator and denominator.

=  3364

Step 2 :

Decompose the number inside the radical sign into prime factors. 

=  3(1 ⋅ 1 ⋅ 1) / 3(4 ⋅ 4 ⋅ 4)

Step 3 :

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign. 

=  1/4

Problem 5 :

Find the square root of (36/81). 

Solution :

Step 1 :

(36/81)

Distribute the square root to numerator and denominator. 

=  √36 / 81

Step 2 :

Decompose the number inside the radical sign into prime factors. 

=  √(2 ⋅ 2 ⋅ 3 ⋅ 3√(3 ⋅ 3 ⋅ 3 ⋅ 3)

Step 3 :

Since the index is 2, we have to take one number out of radical sign for every two same numbers multiplied inside the radical sign. 

=  (⋅ 3) / (3 ⋅ 3)

=  2/3

Problem 6 :

Find the square root (81/100). 

Solution : 

Step 1 :

(81/100)

Distribute the square root to numerator and denominator. 

=  √(81/100)

=  √81 / √100

Step 2 :

Decompose the number inside the radical sign into prime factors. 

=  √(3 ⋅ 3 ⋅ 3 ⋅ 3√(10 ⋅ 10)

Step 3 :

Since the index is 2, we have to take one number out of radical sign for every two same numbers multiplied inside the radical sign. 

=  (⋅ 3) / (3 ⋅ 3)

=  2/3

Problem 7 :

Find the cube root of (125/216). 

Solution :

Step 1 :

3(125/216)

Distribute the cube root to numerator and denominator.

=  3125 3216

Step 2 :

Decompose the numbers inside the radical sign into prime factors. 

=  3(5 ⋅ 5 ⋅ 5) / 3(6 ⋅ 6 ⋅ 6)

Step 3 :

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign. 

=  5/6

Problem 8 :

Find the cube root of (27/343). 

Solution :

Step 1 :

3(27/343)

Distribute the cube root to numerator and denominator. 

=  327 3√343

Step 2 :

Decompose the number inside the radical sign into prime factors. 

=  3(3 ⋅ 3 ⋅ 3) / 3(7 ⋅ 7 ⋅ 7)

Step 3 :

Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign. 

=  3/7

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Problems on Finding Derivative of a Function

    Mar 29, 24 12:11 AM

    Problems on Finding Derivative of a Function

    Read More

  2. How to Solve Age Problems with Ratio

    Mar 28, 24 02:01 AM

    How to Solve Age Problems with Ratio

    Read More

  3. AP Calculus BC Integration of Rational Functions by Partical Fractions

    Mar 26, 24 11:25 PM

    AP Calculus BC Integration of Rational Functions by Partical Fractions (Part - 1)

    Read More