How do you rationalize the denominator and simplify #7/(sqrt3-sqrt2)#?

1 Answer
May 8, 2016

Answer:

Multiply both numerator and denominator by #sqrt(3)+sqrt(2)# to find:

#7/(sqrt(3)-sqrt(2)) = 7sqrt(3)+7sqrt(2)#

Explanation:

Note that #(a-b)(a+b) = a^2-b^2#

So: #(sqrt(3)-sqrt(2))(sqrt(3)+sqrt(2)) = 3 - 2 = 1#

So we find:

#7/(sqrt(3)-sqrt(2)) = (7(sqrt(3)+sqrt(2)))/((sqrt(3)-sqrt(2))(sqrt(3)+sqrt(2))) = 7sqrt(3)+7sqrt(2)#