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Question Number 85864 by john santu last updated on 26/Mar/20

$$simplifytheexpression$$$$\sqrt{6+2\sqrt{8\sqrt{3}-10}}-\sqrt{7-\sqrt{3}}in$$$$theform\sqrt{\sqrt{a}+b}?$$

Answered by jagoll last updated on 26/Mar/20

$$\mathrm{by}\mathrm{trick}!$$$$8\sqrt{3}-10=7\sqrt{3}+\sqrt{3}-7-3$$$$=7(\sqrt{3}-1)-\sqrt{3}(\sqrt{3}-1)$$$$=(7-\sqrt{3})(\sqrt{3}-1)$$$$\mathrm{let}\sqrt{7-\sqrt{3}}=\mathrm{x}\mathrm{and}\sqrt{\sqrt{3}-1}=\mathrm{y}$$$${\mathrm{x}}^2+{\mathrm{y}}^2=7-\sqrt{3}+\sqrt{3}-1=6$$$$\mathrm{hence}\mathrm{a}=3\mathrm{\&}\mathrm{b}=-1$$

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