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nth Root of a

We will discuss here about the meaning of n√a.

The expression n√a means ‘nth rrot of a’. So, (n√a)^n = a.

Also, (a1/a)n = a n × 1/n = a1 = a.

So, n√a = a1/n.


Examples:

1. 3√8 = 81/3

          = (23)1/3

          = 23 × 1/3

          = 21

          = 2.

2. 4√9 = 91/4

          = (32)¼   

          = 32 × ¼

          = 31/2

          = √3.

Note: 31/2 = 2√3. But 2√3 is also written as √3.

nth Root of a

Solved examples on nth Root of a:

Express each of the following in the simplest form without radicals:

(i) 4√52

(ii) n√xm

(iii) 3√64−4


Solution:

(i) 4√52 = (52)1/4

             = 52 × 1/4

(ii) n√xm = (xm)1/n

              = xm × 1/n

              = xm/n.

(iii) 3√64−4 = (64-4)1/3

                 = 64-4 × 1/3

                 = 64-4/3

                 = (43)-4/3

                 = 43(-4/3)

                 = 4-4

                 = 14×4×4×4

                 = 1256.






9th Grade Math

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