How do you simplify #14/ (sqrt7 - sqrt5)#?

1 Answer
Lovecraft
Oct 1, 2015

#7(sqrt(7)+sqrt(5))#

Explanation:

Multiply the numerator and the denominator by the denominator's conjugate, to make the denominator a difference of squares

#14/(sqrt(7) - sqrt(5))*(sqrt(7)+sqrt(5))/(sqrt(7)+sqrt(5)) = (14(sqrt(7)+sqrt(5)))/(7-5)#

Simplify
#(14(sqrt(7)+sqrt(5)))/(7-5) = (14(sqrt(7)+sqrt(5)))/(2) = 7(sqrt(7)+sqrt(5))#

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