How do you simplify $(4+sqrt2)/(3+2sqrt3)$ ?

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Answer 1 · 2018-04-15T18:07:57

I think you're asking for rationalizing?
Answer: $-12+11sqrt(2)-2sqrt(6)$

You rationalize it by multiply both numerator and denominator with its conjugate, which is: $3-sqrt(2)$

$(4+sqrt(2))/(3+sqrt(2)) ((3+sqrt(2))/(3+sqrt(2)))$
$=(12+3sqrt(2)-8sqrt(2)-2sqrt(2)sqrt(3))/(3^2-4(3)$
$=-(12-5sqrt(2)-2sqrt(6))/3$

How do you simplify (4+sqrt2)/(3+2sqrt3)(4+sqrt2)/(3+2sqrt3)?