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Question Number 185325 by Ml last updated on 20/Jan/23

Answered by aleks041103 last updated on 20/Jan/23

$$14+8\sqrt{3}=14+2.2\sqrt{2}.\sqrt{6}=$$$$={\left(\sqrt{6}\right)}^2+{\left(2\sqrt{2}\right)}^2+2\left(2\sqrt{2}\right)\left(\sqrt{6}\right)=$$$$={(\sqrt{6}+2\sqrt{2})}^2$$$$\Rightarrow \sqrt{14+8\sqrt{3}}=\sqrt{{(\sqrt{6}+2\sqrt{2})}^2}=\sqrt{6}+2\sqrt{2}$$$$\Rightarrow b=\sqrt{6}$$$$\Rightarrow 2\sqrt{3}.\sqrt{6}=6\sqrt{2}$$$$\Rightarrow Ans.2b\sqrt{3}=6\sqrt{2}$$

Answered by HeferH last updated on 20/Jan/23

$$\sqrt{2}\cdot \sqrt{7+2\cdot 2\sqrt{3}}-2\sqrt{2}=b$$$$\sqrt{2}\cdot \sqrt{4+3+2\cdot 2\sqrt{3}}-2\sqrt{2}=b$$$$\sqrt{2}\cdot \sqrt{{(2+\sqrt{3})}^2}-2\sqrt{2}=b$$$$2\sqrt{2}+\sqrt{6}-2\sqrt{2}=b$$$$b=\sqrt{6}\Rightarrow b\cdot 2\sqrt{3}=6\sqrt{2}$$

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