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

1 Answer
Apr 7, 2016

Answer:

#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#