Write \sqrt[5]{96}in the simplest form or as \sqrt[n]{b}

Question

Write
`\sqrt[5]{96}`in the simplest form or as
`\sqrt[n]{b}`

Answer 1

Given the radical

`^5\sqrt[]{96}`

Let's take a look first at the possible factors for 96 that have a perfect 5th root. 2 is the 5th root of 32. If we take a look at number 96, we can break it down as 32 x 3. Hence, the radical above can be rewritten as

`^5\sqrt[]{96}=^5\sqrt[]{32*3}`

And since the 5th root of 32 is 2, we can write this as

`^5\sqrt[]{32*3}=^5\sqrt[]{2^5*3}`

By properties of radicals, we can separate the term above as

`^5\sqrt[]{2^(^5)}*^5\sqrt[]{3}`

Simplifying the term above, we get

`2*^5\sqrt[]{3}`

Which is the simplest form of the given radical.