# MULTIPLICATION AND DIVISION OF SURDS WORKSHEET

## About "Multiplication and division of surds worksheet"

Multiplication and division of surds worksheet :

Here we are going to see some practice questions on multiplication and division of surds.

(1)  Simplify the following √5   √18

(2)  Simplify the following ∛13  ∛5

(3)  Simplify the following ∛7  ∛8

(4)  Simplify the following ∜32 ⋅ ∜8

(5)  Simplify the following 3√35 ÷ 2√7

(6)  Simplify the following 15√54 ÷ 3√6

(7)  Simplify the following ∛128 ÷ ∛64

(8)  Simplify the following ∜8 ⋅ ∜12

(9)  Simplify the following 6∜16 ÷ ∜81

(10)  Simplify the following ∜256  ∜81

## Multiplication and division of surds worksheet - Solution

Question 1:

Simplify the following √5   √18

Solution :

=  √5  √18

According to the laws of radical,

=  √(5  18)

=  √(5  3   2

=  3 √(5 ⋅ 2)

=  3√10

Question 2 :

Simplify the following ∛13  ∛5

Solution :

=  ∛13  ∛5

According to the laws of radical,

=  ∛(13 ⋅ 5)  =  ∛65

Question 3 :

Simplify the following ∛7  ∛8

Solution :

=  ∛7  ∛8

According to the laws of radical,

= ∛(7 x 8) ==> ∛(7  2  2  2) ==> 2 ∛(7  2) ==> 2 ∛14

Question 4 :

Simplify the following ∜32 ⋅ ∜8

Solution :

=  ∜32 ⋅ ∜8

=  ∜(32 ⋅ 8)

=  ∜(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

=  (2 ⋅ 2)

=  4

Question 5 :

Simplify the following 3√35 ÷ 2√7

Solution :

=   3√35 ÷ 2√7

According to the laws of radical,

=  (3/2) √(35/7) ==> (3/2)√5

Question 6 :

Simplify the following 15√54 ÷ 3√6

Solution :

=   15√54 ÷ 3√6

According to the laws of radical,

=  (15/3)√(54/6)

=  (15/3)√9

=  (15/3) ⋅ 3  =  15

Question 7 :

Simplify the following ∛128 ÷ ∛64

Solution :

=   ∛128 ÷ ∛64

According to the laws of radical,

=  ∛(128/64)

=  ∛2

Question 8 :

Simplify the following ∜8 ⋅ ∜12

Solution :

=  ∜8 ⋅ ∜12

According to the laws of radical,

=  ∜(8/12)

=  ∜(2/3)

Question 9 :

Simplify the following 6∜16 ÷ ∜81

Solution :

=  6∜16 ÷ ∜81

=  6∜(16/81)

=  6∜(2 ⋅ 2 ⋅ 2 ⋅ 2)/(3 ⋅ 3 ⋅ 3 ⋅ 3)

Since we have the order 4, we have to to factor one term for every four same terms.

=  6 ⋅ (2/3)

=  2 ⋅ 2

=  4

Question 10 :

Simplify the following ∜256  ∜81

Solution :

=  ∜256  ∜81

∜(256  81)

=  ∜(4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

=  4 ⋅ 3

=  12

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