Question

What is the square root of 125/2?

Answer 1

It is `sqrt(125/2)=sqrt(5^3/2)=5*sqrt5/sqrt2`

Answer 2

`(5sqrt10)/2`

Explanation:

Start by factoring 125.
`sqrt(125/2)`
`=sqrt((5*5*5)/2)`
`=sqrt((5^3)/2)`

You can already see here that you can bring 5 out.
`sqrt((5^3)/2)`
`=5sqrt(5/2)`

You can rewrite this as:
`(5sqrt5)/sqrt2`

We now need to rationalize this. We can do that by multiplying both the numerator and denominator by a radical that will eliminate the radical in the denominator. In this case, that radical is `sqrt2`.
`(5sqrt5)/sqrt2`
`=(5sqrt5)/sqrt2(sqrt2/sqrt2)`
`=(5sqrt5*sqrt2)/2`
`=(5sqrt10)/2`

You won't be able to simplify it any further. :)