Question

1/ \(\sqrt{2-\sqrt{3}}\)

2/ \(\sqrt{4+\sqrt{15}}\)

3/ \(\sqrt{6+\sqrt{35}}\)

4/ \(\sqrt{7-3\sqrt{5}}\)

Answer 1

1/ \(\sqrt{2-\sqrt{3}}=\frac{\sqrt{3-2.\sqrt{3}.1+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}.\text{do }\sqrt{3}-1>0\) nên

\(=\frac{\sqrt{3}-1}{\sqrt{2}}\) (sai thì thôi nha)

2) \(\sqrt{4+\sqrt{15}}=\frac{\sqrt{5+2\sqrt{5}.\sqrt{3}+3}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}\) (do \(\sqrt{5}+\sqrt{3}>0\))

Còn lại tương tự