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

$$Simplify:$$$$\frac{\sqrt{2}\cdot \sqrt{2+\sqrt{2}}\cdot \sqrt{2-\sqrt{2}}}{\sqrt{2\sqrt{2}}}=?$$

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

$$thankyouSer$$

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