Question

How do you simplify `sqrt(14)/sqrt(21)`?

Answer 1

Note that `14=2*7and 21=3*7`

Explanation:

We can now rewrite:

`sqrt14=sqrt(2*7)=sqrt2*sqrt7`, and:
`sqrt21=sqrt(3*7)=sqrt3*sqrt7`

Putting this together, we get:

`=(sqrt2*cancelsqrt7)/(sqrt3*cancelsqrt7)=sqrt2/sqrt3`

If you multiply both halves of the fraction by `sqrt3`:

`=(sqrt3*sqrt2)/(sqrt3*sqrt3)=sqrt6/3=1/3 sqrt6`