Question

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

Answer 1

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`