MULTIPLICATION AND DIVISION OF SURDS WORKSHEET

(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

Answers

Question 1:

Simplify the following √5 ⋅  √18

Solution :

  =  √5 ⋅ √18

According to the laws of radical,

  =  √(5 ⋅ 18) 

   =  √(5 ⋅ 3 ⋅ 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

Related topics

• Rationalization of surds
• Comparison of surds
• Operations with radicals
• Ascending and descending  order of surds
• Simplifying radical expression
• Exponents and powers

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