Question

Express the following numbers in index form.
(1) Fifth root of 13 (2) Sixth root of 9 (3) Square root of 256
(4) Cube root of 17 (5) Eighth root of 100 (6) Seventh root of 30

Answer 1

Dear student,

Solution:

Index form of numbers given:

(1) Fifth root of 13 = $\sqrt[5]{13}$

it can also be written as $13^{\frac{1}{5}}$

(2) Sixth root of 9 = $\sqrt[6]{9}$

it can also be written as $9^{\frac{1}{6}}$

(3) Square root of 256 = $\sqrt{256}$

it can also be written as $256^{\frac{1}{2}}$

(4) Cube root of 17= $\sqrt[3]{17}$

it can also be written as $17^{\frac{1}{3}}$

(5) Eighth root of 100 = $\sqrt[8]{100}$

it can also be written as $100^{\frac{1}{8}}$

(6) Seventh root of 30= $\sqrt[7]{30}$

it can also be written as $30^{\frac{1}{7}}$

hope it helps you.

Answer 2

1) Fifth root of 13 = (13)^(1/5) (Ans)

2) Sixth root of 9 = (9)^(1/6) = (3^2)^(1/6) = (3)^(`1/3) (Ans) [2 x 1/6 = 1/3]

3) Square root of 256 = 256^(1/2) = (16^2)^(1/2) = 16 = 2^4 (Ans)

4) Cube root of 17 = 17^(1/3) (Ans)

5) Eighth root of 100 = 100^(1/8) = (10^2)^(1/8) = 10^(1/4) (Ans)

6) Seventh root of 30 = 30^(1/7) (Ans)