How do you rationalize the denominator and simplify #sqrt21/sqrt55#?

1 Answer
Zor Shekhtman
Apr 9, 2015

The fraction does not change if both numerator and denominator are multiplied by the same number.
Multiply them by #sqrt(55)#.
The result will be
#[sqrt(21)*sqrt(55)]/[sqrt(55)*sqrt(55)]=[sqrt(21)*sqrt(55)]/[sqrt(55)^2]#

The denominator is now equal to #55# since the definition of #sqrt(55)# is a number, which produces #55# if squared.

As for numerator, we can use the following property of square root for any two non-negative numbers:
#sqrt(A)*sqrt(B)=sqrt(A*B)#
Using this property, we can represent the numerator as
#sqrt(21)*sqrt(55)=sqrt(21*55)=sqrt(1155)#

The final expression is
#sqrt(1155)/55#

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