Question

Rút gọn biểu thức

 \(\sqrt{14+6\sqrt{5}}-\sqrt{\frac{\sqrt{5}-2}{\sqrt{5}+2}}\)

Answer 1

\(\sqrt{14+6\sqrt{5}}-\sqrt{\frac{\sqrt{5}-2}{\sqrt{5}+2}}=5\)

Answer 2

\(\sqrt{14+6\sqrt{5}}-\sqrt{\frac{\sqrt{5-2}}{\sqrt{5}+2}}=5\)

Answer 3

\(=\sqrt{9+2.3.\sqrt{5}+5}-\sqrt{\frac{\left(\sqrt{5}-2\right)^2}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}}=\sqrt{\left(3+\sqrt{5}\right)^2}-\sqrt{\frac{\left(\sqrt{5}-2\right)^2}{5-4}}\)

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