APPROACH #1: Use conjugate

Given: 2/(2 - √2)

Our goal is to rationalize ("fix") the denominator so that it doesn't have a root.
We'll do this by multiplying the numerator and denominator by the conjugate of 2 - √2, which is 2 + √2

Numerator: 2(2 + √2) = 4 + 2√2
Denominator: (2 - √2)(2 + √2) = 4 - 2 = 2

So, 2/(2 - √2) = (4 + 2√2)/2 = 2 + √2

Answer: D

APPROACH #2: Use calculator
Evaluate \(\frac{2}{2- \sqrt{2}}\) to get 3.414

Then evaluate each answer choice until you get 3.414

Answer: D