How do you simplify #sqrt(15/36)#?

1 Answer
George C.
May 3, 2017

#sqrt(15/36) = sqrt(15)/6#

Explanation:

Here are a couple of identities we will use:

If #a >= 0# and #b > 0# then:

#sqrt(a/b) = sqrt(a)/sqrt(b)#

If #a >= 0# then:

#sqrt(a^2) = a#

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Example

When given #sqrt(15/36)# to simplify, you could simplify #15/36# first, split the square root, then rationalise the denominator, but that would be missing out on the fact that #36=6^2# is already a perfect square.

Instead, we can proceed as follows:

#sqrt(15/36) = sqrt(15/6^2) = sqrt(15)/sqrt(6^2) = sqrt(15)/6#

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