How do you simplify #sqrt15/(2sqrt20)#?

1 Answer
Y
May 10, 2017

Take squares out of square roots.

Explanation:

Original expression: #sqrt(15)/(2sqrt(20))#

Using prime factorization for the values inside the square roots:
#=sqrt(3*5)/(2sqrt(2^2*5)#

Take out the #2^2# out of the square root in the denominator:
#=sqrt(3*5)/(4sqrt(5))#

Combine the square roots into one square root:
#=1/4sqrt((3*5)/5)#

Cancel the #5# in the numerator and denominator of the square root:
#=sqrt(3)/4# which is our final answer.

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