^3√80 in simplest Radical form?

2 Answers
Feb 22, 2018

2root(3)10

Explanation:

I'm guessing that the problem is a cube root? Let me know if it's not. Assuming it's a cube root:

You need to look for perfect cube factors of 80. Perfect cubes are 8, 27, 64, 125, etc. Since 8 is a factor of root(3)80, we can re-write the cube root like this:

root(3)80=root(3)8xxroot(3)10

Now simplify the perfect cube:

root(3)8xxroot(3)10=2xxroot(3)10=2root(3)10

Feb 22, 2018

3\sqrt{80}=12\sqrt{5}

Or

root(3){80}=2root[3]{10}

Explanation:

3\sqrt{80}

=3\sqrt{2\times 2\times 2\times 2\times 5}

Apply the exponent rule to get:

=3\sqrt{2^2\times 2^2\times 5}

Separate each radical to get:

=3\cdot \sqrt{2^2}\cdot \sqrt{2^2}\sqrt{5}

Cancel out the radical to get:

=3\cdot 2\cdot 2\sqrt{5}

Simplify:

=12sqrt{5}

If you input is root(3){80} , then the answer would be:

=2root[3]{10}