How do you rationalize the denominator and simplify # sqrt30/sqrt5#?

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Answer 1 · 2016-09-03T16:48:36

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

You can easily see that #30=5*6#, so

#sqrt(30)/sqrt(6)=sqrt(5*6)/sqrt(5)=(sqrt(5)*sqrt(6))/sqrt(5)=sqrt(6)#

Answer 2 · 2016-09-03T16:51:50

#sqrt(6)#

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

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

#=(sqrt(6)timessqrt(5))/sqrt(5)#

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

#=sqrt(6)#