How do you simplify square root of 70 / square root of 40?

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Answer 1 · 2015-09-19T01:18:10

#sqrt(70) / sqrt(40) = sqrt(7)/2#

Using prime factorization, #sqrt(70) / sqrt(40)# can be rewritten as #sqrt(7*5*2) / sqrt(5*2^3#

#sqrt(5*2)# is found in both the numerator and denominator and cancel each other out:

#sqrt(7*5*2) / sqrt(5*2^3) = sqrt(7) / sqrt( 2^2) #

The denominator #sqrt( 2^2) #, or #sqrt(4)#, is a perfect square which simplifies to #2#:

#sqrt(7) / sqrt( 2^2) = sqrt(7)/2#

This is the simplified expression.