Question

How do you rationalize the denominator and simplify `sqrt36/sqrt8`?

Answer 1

`sqrt36/sqrt8=(3sqrt2)/2`

Explanation:

To rationalize the denominator in `sqrt36/sqrt8`, let us examine the denominator.

As `sqrt8=sqrt(2xx2xx2)=2sqrt2`, if we multiply this by `sqrt2`, it will become rational.

Hence multiplying numerator and denominator by`sqrt2` we get

`sqrt36/sqrt8=(sqrt36xxsqrt2)/(sqrt8xxsqrt2)`

= `(6sqrt2)/(sqrt16)=(6sqrt2)/4=(3cancel(6)sqrt2)/(2cancel4)=(3sqrt2)/2`