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Question Number 183041 by Shrinava last updated on 18/Dec/22

$$\mathrm{Find}:$$$$\sqrt{12-2\sqrt{35}}-\sqrt{10-2\sqrt{21}}=?$$

Answered by HeferH last updated on 18/Dec/22

$$\sqrt{12-2\sqrt{35}}=\sqrt{{\left(\sqrt{7}\right)}^2+{\left(\sqrt{5}\right)}^2-2\sqrt{7}\cdot \sqrt{5}}$$$$\Rightarrow \sqrt{{(\sqrt{7}-\sqrt{5})}^2}=\sqrt{7}-\sqrt{5}$$$$\sqrt{10-2\sqrt{21}}=\sqrt{{\left(\sqrt{7}\right)}^2+{\left(\sqrt{3}\right)}^2-2\sqrt{7}\cdot \sqrt{3}}$$$$\Rightarrow \sqrt{{(\sqrt{7}-\sqrt{3})}^2}=\sqrt{7}-\sqrt{3}$$$$\sqrt{7}-\sqrt{5}-(\sqrt{7}-\sqrt{3})=\sqrt{3}-\sqrt{5}$$

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