How do you simplify (2sqrt3+sqrt2)/(sqrt3+2sqrt2)2√3+√2√3+2√2?

1 Answer
Alan P.
Apr 3, 2015

Multiply both numerator (top) and denominator (bottom) by the conjugate (see example) of the denominator.

(2sqrt(3)+sqrt(2))/(sqrt(3)+2sqrt(2))*(sqrt(3)-2sqrt(2))/(sqrt(3)-2sqrt(2))2√3+√2√3+2√2⋅√3−2√2√3−2√2

= (2(3) +sqrt(2)sqrt(3)-4sqrt(2)sqrt(3)-2(2))/(3-8)=2(3)+√2√3−4√2√3−2(2)3−8

=(10 - 3sqrt(6))/(-5)=10−3√6−5

= 3/5sqrt(6) -2=35√6−2

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