^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}#