Question

What is 3 square root of 125x12?

Answer 1

Hi!

Square roots where the things under the root are multiplied (for example $\sqrt{xy}$) can be split up into $\sqrt{x} * \sqrt{y}$.

That's what I'm going to do in this case. I'm going to split $\sqrt[3]{125x^{12}}$ into $\sqrt[3]{125} * \sqrt[3]{x^{12}}$

Now, the cube root of 125 is 5, because 5 * 5 * 5 = 125, and that is the definition of a cube root. (What multiplied 3 times by itself is equal to what's under the root)

Now to look at what the cube root of $x^{12}$ is.

A cube root can be rewritten as $x^{\frac{1}{3}}$, same as a square root can be rewritten to $x^{\frac{1}{2}}$.

So if you take the cube root of x^12, you can change it to:

$(x^{12} )^{1/3}$

If you have a case like this, then you can multiply the two powers (in this case 12 and 1/3) to simplify it. 12 * 1/3 = 4, so you get x^4.

Now putting the two together, you get:

5$x^{4}$ as your answer.

Hope this helped!

Answer 2

Cube root of of 125 is 5
cube root ofx^12 is x^4

so the answer is 5*x^4 or second choice