Question

[Vũ Hùng Việt]

Tính

a)  \(\left(2+\sqrt{5}\right)\sqrt{7-4\sqrt{3}}-\sqrt{\left(-3\right)^2}\)

b) \(\frac{\sqrt{26}}{\sqrt{13}}-\frac{2+\sqrt{2}}{\sqrt{x}+1}-\frac{2}{\sqrt{x}-3}\)

c) \(\frac{1}{2\sqrt{3}}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{3}-1}-\sqrt{7-2\sqrt{6}}\)

Answer 1

[Nguyễn Huy Tú]

a, \(\left(2+\sqrt{5}\right)\sqrt{7-4\sqrt{3}}-\sqrt{\left(-3\right)^2}\)

\(=\left(2+\sqrt{5}\right)\sqrt{\left(2-\sqrt{3}\right)^2}-3\)

\(=\left(2+\sqrt{5}\right)\left(2-\sqrt{3}\right)-3=1-2\sqrt{3}+2\sqrt{5}-\sqrt{15}\)

b, đề sai ko bạn ? 

c, \(\frac{1}{2\sqrt{3}}-\frac{\sqrt{6}-\sqrt{2}}{\sqrt{3}-1}-\sqrt{7-2\sqrt{6}}\)

\(=\frac{2\sqrt{3}}{12}-\frac{\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}-\sqrt{\left(\sqrt{6}-1\right)^2}\)

\(=\frac{\sqrt{3}}{6}-\sqrt{2}-\sqrt{6}+1=\frac{\sqrt{3}-6\sqrt{2}-6\sqrt{6}+6}{6}\)