How do you rationalize the denominator and simplify $2/(sqrt3+sqrt2)$ ?

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Answer 1 · 2016-03-26T14:40:43

$= 2(sqrt3 - sqrt2)$

$2 / (sqrt3 + sqrt2)$

We rationalise the expression by multiplying it with the conjugate of the denominator.

Conjugate of $color(blue)(sqrt3 + sqrt 2= sqrt 3 - sqrt2$

$(2 * color(blue)((sqrt 3 - sqrt2))) / ((sqrt3 + sqrt2) * color(blue)((sqrt 3 - sqrt2))$

Applying property :- $color(green)((a+b)(a-b) = a^2 - b^2$ , to the denominator.

$=(2 * color(blue)((sqrt 3)) + 2 * color(blue)( (- sqrt2))) / ((sqrt3)^2 - (sqrt2)^2$

$= (2sqrt3 - 2sqrt2) / ( 3-2)$

$= (2(sqrt3 - sqrt2)) / 1$

$= 2(sqrt3 - sqrt2)$

How do you rationalize the denominator and simplify 2/(sqrt3+sqrt2)2/(sqrt3+sqrt2)?