Question

How do you rationalize the denominator and simplify `sqrt(245/3)`?

Answer 1

`sqrt(245/3)=(7sqrt15)/3`

Explanation:

`sqrt(245/3)=sqrt245/sqrt3`

As we have `sqrt3` in denominator, we need to multiply it by `sqrt3`, that will make the denominator `sqrt9=3` and thus rationalise the denominator. But as we multiply denominator by `sqrt3`. we should also multiply numerator by `sqrt3`. Hence,

`sqrt(245/3)=sqrt245/sqrt3`

= `(sqrt245×sqrt3)/(sqrt3×sqrt3`

= `sqrt735/3`

= `sqrt(3×5×ul(7×7))/3`

= `(7sqrt15)/3`