sqrt((48x^4))?

sqrt((48x^4))

2 Answers
Feb 28, 2018

4x^2\sqrt{3}

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}

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

So that get:

=4x^2\sqrt{3}

That's it!

Feb 28, 2018

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.