INDEX FORM OF SURD

About "Index form of surd" 

Index Form of Surd :

The index form of a surd n√a is a1/n

For example, ∛5 can be written in index form as

∛5  = 5 1/3

What is surd ?

If ‘a’ is a positive rational number and n is a positive integer such that na is an irrational number, then nis called a ‘surd’ or a ‘radical’.

The general form of a surd is na is "√" is called a radical sign n is called the order of the radical and "a" is called radicand.

In the following table, the index form, order and radicand of some surds are given.

Surd

Index form

Order

Radicand

√5

14

∜7

√50

51/2

141/3

71/4

501/2

2

3

4

2

5

14

7

50

Let us look into some examples based on the above concept.

Example 1 :

Convert the following surds into index form

√7 

Solution :

Radical form  =  √7 

Index form  =  71/2

Example 2 :

Convert the following surds into index form

∜8 

Solution :

Radical form  =  ∜8 

Index form  =  81/4

Example 3 :

Convert the following surds into index form

∛6 

Solution :

Radical form  =  ∛6 

Index form  =  61/3

Example 4 :

Convert the following surds into index form

8√7 

Solution :

Radical form  =  8√7 

Index form  =  71/8

Surds and indices formulas

(1)   (n√a) =  a

(2)  n√a x n√b  =  n√(a x b)

(3)  n√a / n√b  =  n√(a / b)

(4)  (n√a) =  am/n

Let us look into some examples based on above formulas.

Example 1 :

Simplify the following

√5  √18

Solution :

We have two radicals with same order, so we may take one radical and multiply the terms

√5  √18  =  √(5  18)

  =  √(5  3 ⋅ 3 ⋅ 2)

=  3 (5  2)

=  3√10

Example 2 :

Simplify the following

3√35 ÷ 2√7

Solution :

We have two radicals with same order, so we may take one radical and divide the terms

3√35 ÷ 2√7  =  (3/2) ⋅ √(35/7)

  =  (3/2) ⋅ √5

  =  3√5/2

Example 3 :

Simplify the following

4√8 ÷ 4√12

Solution :

We have two radicals with same order, so we may take one radical and divide the terms

4√8 ÷ 4√12  =  4√(8/12)

  =  4√(2/3)

  =  4√2 / 4√3

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