Question

^3√80 in simplest Radical form?

Answer 1

`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`

Answer 2

`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}`