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

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Answer 1 · 2016-04-07T06:50:16

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

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

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

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

How do you rationalize the denominator and simplify sqrt36/sqrt8sqrt36/sqrt8?