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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