How do you simplify #\frac { 3\sqrt { 3} + \sqrt { 2} } { 3- 4\sqrt { 5} }#?

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Answer 1 · 2018-05-18T21:57:04

rationalize the denominator

You multiply it times its radical conjugate:

#(3+4sqrt5)/(3+4sqrt5) = 1#

Because the numerator and denominator are the same. So it won't change the value when you multiply it times the original expression:

#(3sqrt3+sqrt2)/(3-4sqrt5) * (3+4sqrt5)/(3+4sqrt5)#

then FOIL the top and bottom.

#(9sqrt3 +12sqrt15 + 3sqrt2 + 4sqrt10)/(9 +12sqrt5 - 12 sqrt5 -16*5#

#(9sqrt3 +12sqrt15 + 3sqrt2 + 4sqrt10)/(71#