Question

How do you simplify `3/sqrt(7)`?

Answer 1

`(3sqrt7)/7`

Explanation:

Simplifying this fraction means expressing it without the radical on the denominator. This is called `color(blue)"rationalising the denominator"`

To do this we make use of the following fact.

`color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=(sqrta)^2=a)color(white)(a/a)|)))`

`rArrsqrt7xxsqrt7=7`

Since this is a fraction, if we multiply the denominator by some value then we must multiply the numerator by the same value.

multiply both numerator and denominator by `sqrt7`

`rArr3/sqrt7xxsqrt7/sqrt7=(3xxsqrt7)/(sqrt7xxsqrt7)=(3sqrt7)/7`