Can you help me simplify this radical? Please!?

Question

This is in fraction format. The ---- is the division line. Imagine the √() is the radical sign.

√(48n^6)

-------------

√(6n^3)

Can someone explain please!?

Answer 1

Sqrt(48n^6)

-----------------  means sqrt(48n^6/6n^3)

Sqrt(6n^3)

=>sqrt(48/6*n^6/n^3)

=>sqrt(8*n^(6-3))

=>sqrt(8*n^3)

=>sqrt(2^3*n^3)

=>sqrt((2n)^3)

Are you sure it is a square root and not a cube root?

If it's a cube root you can go further and do this

cuberoot((2n)^3) means ((2n)^3)^1/3

=>2n

If it's a square root though, the final answer would just be ((2n)^3)^1/2

or the square root of (2n) cubed