What is the square root of 14 divided by the square root of 45?

1 Answer
Alan P.
Oct 18, 2015

(Nothing really pretty)
#sqrt(14)/sqrt(45) = sqrt(21)/9#

Explanation:

#sqrt(14)/sqrt(45)#

Factoring:
#color(white)("XXXX")=(cancel(sqrt(2))*sqrt(7))/(sqrt(3)*sqrt(3)*sqrt(3)*cancel(sqrt(2)))#

Simplifying:
#color(white)("XXXX")=sqrt(7)/(3sqrt(3))#

Rationalizing the denominator (by multiplying both numerator and denominator by #(sqrt(3))#
#color(white)("XXXX")=sqrt(21)/9#

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