What is the value of 2/(2−√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

We have \(\frac{2}{2-\sqrt{2}}\)

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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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

We can simplify the expression by multiplying by (2 + √2)/(2 + √2), and we have:

(4 + 2√2)/(2^2 - (√2)^2)

(4 + 2√2)/(4 - 2)

(4 + 2√2)/2

2 + √2

Answer: D