Simplify #3sqrt(125/36)#?

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Answer 1 · 2017-03-29T03:53:22

#(5sqrt(5))/2#

I'm reading this as #3sqrt(125/36)#

First thing to do is see that we can rewrite the terms under the square root sign into terms that have perfect squares:

#3sqrt((5xx25)/36)#

#3((sqrt(5)xxsqrt(25))/sqrt36)#

Let's take square roots of the perfect squares:

#3xx(sqrt(5)xx5)/6#

#(3xxsqrt(5)xx5)/6#

Let's cancel the 6 in the denominator against the 3 in the numerator and reorder the terms:

#(5sqrt(5))/2#