How do you simplify #sqrt(49)/sqrt(500)#?

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Answer 1 · 2016-01-29T22:18:42

#sqrt(49)/sqrt(500)=7/(10sqrt(5))=(7sqrt(5))/50#

We will use the following properties:

#sqrt(49)/sqrt(500) = sqrt(7^2)/sqrt(10^2*5)#

#=7/(sqrt(10^2)sqrt(5))#

#=7/(10sqrt(5))#

We could finish here, or rationalize the denominator by multiplying the numerator and denominator by #sqrt(5)# to obtain

#7/(10sqrt(5)) = (7sqrt(5))/(10sqrt(5)sqrt(5))#

#=(7sqrt(5))/(10*5)#

#=(7sqrt(5))/50#