Question

`sqrt((48x^4))`?

`sqrt((48x^4))`

Answer 1

`4x^2\sqrt{3}`

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Explanation:

`\sqrt{48x^4}`

Apply the product of radical rule `\root[n]{ab}=\root[n]{a}\cdot \root[n]{b}`

`=\sqrt{48}\sqrt{x^4}`

`=\sqrt{2\cdot 2\cdot 2\cdot 2\cdot 3}\sqrt{x^4}`

`=\sqrt{2^4\cdot 3}\sqrt{x^4}`

`=\sqrt{2^4}\sqrt{x^4}\sqrt{3}`

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By using the radical rule `\root[n]{a^m}=a^{\frac{m}{n}}`, we get:

`\sqrt{2^4}=2^{\frac{4}{2}}=2^2=4`
`\sqrt{x^4}=x^{\frac{4}{2}}=x^2`

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So that get:

`=4x^2\sqrt{3}`

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That's it!

Answer 2

`4x^2sqrt3`

Explanation:

First, let's break up the radical into two expressions so it'll be easier to deal with. We get:

`color(blue)sqrt(48)*sqrt(x^4)`

We can factor a perfect square out of `sqrt48`. We can factor out a `16` and `3`. We would get:

`color(blue)sqrt16*color(blue)sqrt3*sqrt(x^4)` (Blue terms are equal to `sqrt48`)

`sqrt16` simplifies to `4`, we cannot factor `sqrt3` any further, and `sqrt(x^4)` would simply be `x^2`. We have:

`4sqrt3*x^2`

We can rewrite this with `x^2` being in front of the radical, and we get:

`4x^2sqrt3`

NOTE: When typing radicals, numbers, exponents and variables, etc., you have to put a hashtag (###) on both ends.