How do you simplify 14 /(sqrt5 + sqrt3)14√5+√3?

1 Answer
Noah G · mason m
Jan 31, 2016

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))14√5+√3

The conjugate would be sqrt(5) - sqrt(3)√5−√3

14/(sqrt(5) + sqrt(3)) xx (sqrt(5) - sqrt(3))/(sqrt(5) - sqrt(3))14√5+√3×√5−√3√5−√3

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

(14sqrt(5) - 14sqrt(3))/(5 - 3)14√5−14√35−3

(14sqrt(5) - 14sqrt(3)) / 214√5−14√32

7sqrt5-7sqrt37√5−7√3

The answer is 7sqrt5-7sqrt37√5−7√3.

Hopefully this helps!

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