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

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Answer 1 · 2016-05-08T22:36:11

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

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

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:

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

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