Question

How do you simplify `sqrt5 div sqrt3`?

Answer 1

`sqrt(15)/3`

Explanation:

`sqrt(5)-:sqrt(3)` can be rewritten as `sqrt(5)/sqrt(3)`.

As there is a surd (radical) on the botoom, we have to rationalise the denominator, to do this we use the equation: `a/sqrt(b)-=(a*sqrt(b))/(sqrt(b)^2)=(asqrt(b))/b`.

In this case, `a=sqrt(5)` and `b=sqrt(3)`. By putting our values in we get: `sqrt(5)/sqrt(3)-=(sqrt(5)*sqrt(3))/(sqrt(3)^2)=(sqrt(5*3))/3=(sqrt(15))/3`. As none of the factors of 15 are perfect squares, this fraction cannot be simplified.