We have \(\frac{2}{2-\sqrt{2}}\)M7MBA wrote:What is the value of \(\frac{2}{2-\sqrt{2}}? \)
(A) 1
(B) 2
(C) 1 + \(\sqrt{2}\)
(D) 2 + \(\sqrt{2}\)
(E) 4
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
Let's rationalize the denominator
Multiplying \(\frac{2}{2-\sqrt{2}}\) by \(\frac{2+\sqrt{2}}{2+\sqrt{2}}\); this will not chnage the value of the fraction.
\(\frac{2}{2-\sqrt{2}}\) * \(\frac{2+\sqrt{2}}{2+\sqrt{2}}\)
\(\frac{4+2\sqrt{2}}{2^2-\sqrt{2^2}}\)
\(\frac{4+2\sqrt{2}}{4-2}\)
\(\frac{4+2\sqrt{2}}{2}\)
\(2+\sqrt{2}\)
The correct answer: D
Hope this helps!
-Jay
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