Question

Tính

\(a.\) \(\sqrt{3+\sqrt{5}}\)

\(b.\) \(\sqrt{7+\sqrt{13}}\)

Mysterious Person

Akai Haruma

Mashiro Shiina

Answer 1

a)Ta có:

\(\sqrt{3+\sqrt{5}}=\dfrac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}+1}{\sqrt{2}}=\dfrac{\sqrt{10}+\sqrt{2}}{2}\)

b) ta có:

\(\sqrt{7+\sqrt{13}}=\dfrac{\sqrt{14+2\sqrt{13}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{13}+1\right)^2}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{13}+1}{\sqrt{2}}=\dfrac{\sqrt{26}+\sqrt{2}}{2}\)

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