IMAT 2020 Question 53

[Juliette]

Hi!

2 / 2+ square root of 3

Answer is 4 - 2 square root of 3

How do we get the answer?

[Ujjwal]

Hi!
We just need to rationalize the denominator. so, basically we have to multiply and divide the expression by 2- square root 3.
2/2+ sq. root three x 2- sq. root three/2- sq. root three
4-2 sq. root three/(2)^2- (root 3)^2
we are left with 4-2sq . root three.
Here’s how Natali solved it:)

IMAT 2020 Q53 [Equal]

To solve this, we must multiply the whole equation with \frac{2-\sqrt3}{2-\sqrt3}, this will allow us to get difference of two squares, which states: a^2 - b^2 = (a-b)(a+b). So by multiplying it, we get: \frac{2 \cdot ( 2-\sqrt3)}{(2+\sqrt3)(2-\sqrt3)} = \frac{4-2\sqrt3}{2^2-(\sqrt3)^2} = \frac{4-2\sqrt3}{4-3} = 4-2\sqrt3. So the correct answer is (B)

Hope it helps:)