Question

How do you simplify `sqrt(5/3)`?

Answer 1

`sqrt(5/3) = sqrt(15)/3`

Explanation:

Note that if `b > 0` then:

`sqrt(a/b) = sqrt(a)/sqrt(b)`

The same is not true if `a > 0` and `b < 0`.

Given to simplify:

`sqrt(5/3)`

The way I have seen most people address this kind of problem is to separate the square root then rationalise the denominator by multiplying both numerator and denominator by `sqrt(3)`, so:

`sqrt(5/3) = sqrt(5)/sqrt(3) = (sqrt(5)sqrt(3))/(sqrt(3)sqrt(3)) = sqrt(15)/3`

Personally, I prefer to multiply the numerator and denominator by `3` first, in order to make the denominator into a perfect square, thus:

`sqrt(5/3) = sqrt(15/3^2) = sqrt(15)/sqrt(3^2) = sqrt(15)/3`