Question

To rationalize the denominator of (5-\sqrt(7))/(9-\sqrt(14)) , you should multiply the expression by which fraction?

Answer 1

You would multiply by


`(9+√(14))/(9+√(14))`.

When you rationalize the denominator, you multiply by the conjugate of the denominator. The conjugate is the same numbers and radicals, but with the sign of the radical switched.

Answer 2

`(9+√(14))/(9+√(14))`

Explanation:

we have

`(5-√(7))/(9-√(14))`

we know that

To rationalize the denominator, multiply by the conjugate of the denominator

so

`(5-√(7))/(9-√(14))*(9+√(14))/(9+√(14))=((5-√(7))(9+√(14)))/(9^(2)-14)\\ \\=((5-√(7))(9+√(14)))/(67)`