Question

How do you simplify `14 /(sqrt5 + sqrt3)`?

Answer 1

This is completely simplified if you want to combine radicals. However, we can simplify further by rationalizing the denomiator.

Explanation:

To rationalize the denomiator, we must multiply the entire expression by the conjugate of the denominator. The conjugate forms a difference of squares with the denominator so to cancel out the radicals.

`14/(sqrt(5) + sqrt(3))`

The conjugate would be `sqrt(5) - sqrt(3)`

`14/(sqrt(5) + sqrt(3)) xx (sqrt(5) - sqrt(3))/(sqrt(5) - sqrt(3))`

`(14sqrt(5) - 14sqrt(3)) / (sqrt(25) + sqrt(15) - sqrt(15) - sqrt(9))`

`(14sqrt(5) - 14sqrt(3))/(5 - 3)`

`(14sqrt(5) - 14sqrt(3)) / 2`

`7sqrt5-7sqrt3`

The answer is `7sqrt5-7sqrt3`.

Hopefully this helps!