ADDITION AND SUBTRACTION OF SURDS WORKSHEET

Addition and subtraction of surds worksheet - Practice questions

(1)  Simplify 10√2 - 2√2 + 4√32

(2)  Simplify √48 - 3√72 - √27 + 5√18

(3)  Simplify ∛16 + 8∛54 - ∛128

(4)  Simplify 7∛2 + 6∛16 - ∛54

The following concepts will help you to solve the problems given above.

Question 1 :

Simplify 10√2 - 2√2 + 4√32

Solution :

10√2 - 2√2 + 4√32  =  10√2 - 2√2 + 4√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)

  =  10√2 - 2√2 + 4(2 ⋅ 2)√2

  =  10√2 - 2√2 + 16√2

  =  (10 + 16 - 2)√2

  =  24 √2

Hence the answer is 24√2.

Question 2 :

Simplify √48 - 3√72 - √27 + 5√18

Solution :

√48 - 3√72 - √27 + 5√18

Let us find the factors the numbers inside the radicals

√48  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2⋅ 3)  =  (2 ⋅ 2)√3  =  4 √3

3√72  =  3√(2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3)  =  (3 ⋅ 2 ⋅ 3)√2  =  18 √2

√27  =  √(3 ⋅ 3 ⋅ 3)  =  3 √3

5√18  =  5√(3 ⋅ 3 ⋅ 2)  =  (5 ⋅ 3) √2  =  15√2

√48 - 3√72 - √27 + 5√18  =  4√3 - 18√2 - 3√3 + 15√2

  =  4√3 - 3√3 - 18√2 + 15√2

  =  1√3 - 3√2

Hence the answer is 1√3 - 3√2.

Question 3 :

Simplify ∛16 + 8∛54 - ∛128

Solution :

∛16 + 8∛54 - ∛128

Let us find the factors the numbers inside the radicals

∛16  =  ∛(2 ⋅ 2 ⋅ 2 ⋅ 2)  =  2∛2

8∛54  =  8 ∛(2 ⋅ 3 ⋅ 3 ⋅ 3)  =  (8 ⋅ 3) ∛2  =  24∛2

∛128  =  ∛(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2)   =  (2 ⋅ 2)∛2  =  4∛2

∛16 + 8∛54 - ∛128  =  2∛2 + 24∛2 - 4∛2

  =  (2 + 24 - 4)∛2

  =  22∛2

Hence the answer is 22∛2. 

Question 4 :

Simplify 7∛2 + 6∛16 - ∛54

Solution :

7∛2 + 6∛16 - ∛54

Let us find the factors the numbers inside the radicals

6∛16  =  6∛(2 ⋅ 2 ⋅ 2 ⋅ 2)  =  (6 ⋅ 2) ∛2  =  12∛2

∛54  =  ∛(2 ⋅ 3 ⋅ 3 ⋅ 3)  =  3 ∛2  =  3∛2

7∛2 + 6∛16 - ∛54  =  7∛2 + 12∛2 - 3∛2

  =  (7 + 12 - 3)∛2

  =  16∛2

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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