Simplify

[mlaboda]

I got this question from a flashcard and my answer isn't matching the test book's answer. Please help.

Simplify:

3/(2+(3^1/2))

[rossmj]

Multiply the fraction by (2-sqrt(3))/(2-sqrt(3)) by using the minus you get an a^2-b^2 situation on the bottom rather than a term with a radical in it.

[gmat740]

It is a simple rationalisation problem

in the denominator you are given : 2-sqrt(3)

try to make it as integer:
best possible way => multiply with conjugate = 2+sqrt(3)

so, we have denominator as,
[2+sqrt(3)]*[2-sqrt(3)]
this is in the form of

(a+b)(a-b) = a^2 - b^2 = 2^2-(sqrt 3)^2 = 4-3 =1

but we have multiplied denominator,so to balance that effect of multiplication,we need to multiply the numerator as well with the same multiple

so,
3(2-sqrt3)

this has to be the answer

You can further solve this as

6 - 3*sqrt(3)

Hope this helps

[mlaboda]

Thanks Karan!