Simplify-2-2-2-2-2-2-2-

Question Number 146964 by mathdanisur last updated on 16/Jul/21

S i m p l i f y :

\frac{\sqrt{2} \cdot \sqrt{2 + \sqrt{2}} \cdot \sqrt{2 - \sqrt{2}}}{\sqrt{2 \sqrt{2}}} = ?

Answered by Olaf_Thorendsen last updated on 16/Jul/21

x = \frac{\sqrt{2} \sqrt{2 + \sqrt{2}} . \sqrt{2 - \sqrt{2}}}{\sqrt{2 \sqrt{2}}}

x = \frac{\sqrt{2} \sqrt{(2 + \sqrt{2}) (2 - \sqrt{2})}}{\sqrt{2 \sqrt{2}}}

x = \frac{\sqrt{2} \sqrt{2}}{\sqrt{2 \sqrt{2}}} = \frac{2}{\sqrt{2 \sqrt{2}}} = \frac{2 \sqrt{2 \sqrt{2}}}{2 \sqrt{2}} = \sqrt{\sqrt{2}} = 2^{\frac{1}{4}}

Commented by mathdanisur last updated on 16/Jul/21

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