Question

rút gọn:

\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

Answer 1

\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}=\sqrt{\left(\sqrt{5}+2\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}+2-\left|\sqrt{5}-2\right|=\sqrt{5}+2-\sqrt{5}+2=4\)

Answer 2

\(=\sqrt{4+4\sqrt{5}+5}-\sqrt{4-4\sqrt{5}+5}\\ =\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\\ =2+\sqrt{5}-\sqrt{5}+2=4\)