Question

Write in the simplest form:-
$\sqrt[5]{320}$
​

Answer 1

Answer:

Simplest form =

$2 \sqrt[5]{10}$

Step-by-step explanation:

Given :

$\sqrt[5]{320}$

To write :

In the simplest form.

Solution :

$320 = 64 \times 5 = {2}^{6} \times 5 = {2}^{5} \times 10$

$\sqrt[5]{320} = \sqrt[5]{ {2}^{5 } \times 10}$

$\sqrt[5]{ {2}^{5} } \times \sqrt[5]{10}$

${ ({2}^{5} )}^{ \frac{1}{5} } \times \sqrt[5]{10} = {2}^{5 \times \frac{1}{5} } \times \sqrt[5]{10}$

$= 2 \sqrt[5]{10}$

Hence, the simplest form.