Question

radical form of 5 power 2/5

Answer 1

Answer:

25√5

Explanation:

Keep this rule in mind:

XXamn=n√am

Now that you know that rule, you can convert it to radical form.

XX552=√55

We can simplify this further:

√55=√54⋅5=52√5=25√5

Answer 2

Answer:

The radical expression of  $5^{\frac{2}{5} }$= $\sqrt[5]{25}$

Step-by-step explanation:

Given number is $5^{\frac{2}{5} }$

To find

the radical form of the given number

Solution

Recall the concept

A radical is defined as the nth root of a particular number.  It is denoted as $\sqrt[n]{a}$

$a^{mn} =( a^m) ^n$ --------------(1)

$a^{\frac{1}{n} = \sqrt[n]{a}$ ----------------------(2)

Given number is $5^{\frac{2}{5} }$

using the identity (1) the given expression $5^{\frac{2}{5} }$  can be expressed as

= $(5^{2}) ^\frac{1}{5}$

= $(25) ^\frac{1}{5}$

Using the identity (2) we get

= $\sqrt[5]{25}$

∴The radical expression of  $5^{\frac{2}{5} }$= $\sqrt[5]{25}$

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