The value of $\frac{2 \sqrt{2}}{2-\sqrt{

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Target Exam

CUET

Subject

General Test

Chapter

Numerical Ability

Topic

Number System (1)

Question:

The value of $\frac{2 \sqrt{2}}{2-\sqrt{2}}$ is:

Options:

$\frac{\sqrt{2}+1}{2}$

$\sqrt{2}+1$

$2(\sqrt{2}+1)$

$2(\sqrt{2}-1)$

Correct Answer:

$2(\sqrt{2}+1)$

Explanation:

\frac{2 \sqrt{2}}{2-\sqrt{2}}

multiply and divide by ( 2 + √2 )

⇒ \frac{2 \sqrt{2}}{2-\sqrt{2}} × \frac{2 + \sqrt{2}}{2+ \sqrt{2}}

⇒ \frac{4 \sqrt{2} + 4 }{2}

= $2(\sqrt{2}+1)$