How do you simplify #sqrt (27 / 64)#?

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Answer 1 · 2016-02-08T18:42:45

#(3sqrt3)/8#

We can begin be re writing the square root as:

#sqrt(27/64) = sqrt(27)/sqrt(64)#

Luckily, 64 is a square number so that will allow us to get rid of the square root on the bottom:

#=sqrt(27)/8#

Now we can transform #sqrt(27)# into a surd like so:

#sqrt(27) = sqrt(9*3) = sqrt(9)*sqrt(3) = 3sqrt3#

So the fraction can be re written as:

#(3sqrt3)/8#