How do you rationalize the denominator and simplify sqrt30/sqrt5305?

2 Answers
Sep 3, 2016

The value of this expression is sqrt(6)6. See explanation.

Explanation:

You can easily see that 30=5*630=56, so

sqrt(30)/sqrt(6)=sqrt(5*6)/sqrt(5)=(sqrt(5)*sqrt(6))/sqrt(5)=sqrt(6)306=565=565=6

Sep 3, 2016

sqrt(6)6

Explanation:

We have: sqrt(30)/sqrt(5)305

Let's begin by expressing the numerator as a product of two radicals:

=(sqrt(6)timessqrt(5))/sqrt(5)=6×55

We can then simlify this expression by cancelling the sqrt(5)5 terms:

=sqrt(6)=6