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

1 Answer
Jan 31, 2016

Answer:

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!