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Question Number 156754 by abdurehime last updated on 15/Oct/21

Answered by MathsFan last updated on 15/Oct/21

$$\sqrt{5+2\sqrt{6}}=\sqrt{5+\sqrt{24}}=\sqrt{\frac{5+\sqrt{1}}{2}}+\sqrt{\frac{5-\sqrt{1}}{2}}=\sqrt{3}+\sqrt{2}$$$$\sqrt{5-2\sqrt{6}}=\sqrt{\frac{5+\sqrt{1}}{2}}-\sqrt{\frac{5-\sqrt{1}}{2}}=\sqrt{3}-\sqrt{2}$$$$i.\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}=2\sqrt{2}$$$$$$$$\mathit{i}\mathit{i}.$$$$\{\begin{array}{l}.\sqrt{7-\sqrt{24}}=\sqrt{\frac{7+5}{2}}-\sqrt{\frac{7-5}{2}}=\sqrt{6}-1\\ \sqrt{7+\sqrt{24}}=\sqrt{6}+1\end{array}$$$$\therefore \frac{\sqrt{6}+1+\sqrt{6}-1}{2}=\frac{2\sqrt{6}}{2}=\sqrt{6}$$$$\mathbf{stay}\mathbf{safe}$$$$\mathbf{stay}\mathbf{blessed}...$$$$$$

Commented by abdurehime last updated on 15/Oct/21

$$\mathrm{please}\mathrm{help}\mathrm{question}4$$

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