How do you rationalize $(2sqrt3-sqrt2)/ (5sqrt2+sqrt3)$ ?

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Answer 1 · 2015-05-10T21:45:36

Given $(2sqrt(3)-sqrt(2))/(5sqrt(2)+sqrt(3))$ , try multiplying both the top and the bottom by $(5sqrt(2)-sqrt(3))$

The numerator:

$(2sqrt(3)-sqrt(2))(5sqrt(2)-sqrt(3))$

$=-2sqrt(3)sqrt(3)+9sqrt(2)sqrt(3)-5sqrt(2)sqrt(2)$

$=-2*3+9sqrt(2*3)-5*2$

$=9sqrt(6)-16$

The denominator:

$(5sqrt(2)+sqrt(3))(5sqrt(2)-sqrt(3))$

$=25sqrt(2)sqrt(2)-sqrt(3)sqrt(3)$

$=50-3$

$=47$ .

So $(2sqrt(3)-sqrt(2))/(5sqrt(2)+sqrt(3)) = (9sqrt(6)-16)/47$ .

How do you rationalize (2sqrt3-sqrt2)/ (5sqrt2+sqrt3)(2sqrt3-sqrt2)/ (5sqrt2+sqrt3)?