Question

Rút gọn biểu thức:

B= \(\sqrt{\frac{10+6\sqrt{3}}{1+\sqrt{3}}}\)

Answer 1

\(B=\sqrt{\frac{\left(10+6\sqrt{3}\right)\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}}=\sqrt{\frac{10\sqrt{3}-10+18-6\sqrt{3}}{2}}\)

\(=\sqrt{\frac{8+4\sqrt{3}}{2}}=\sqrt{4+2\sqrt{3}}\)

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