Question

Rút gọn biểu thức

\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)

Answer 1

=\(\sqrt{\left(2+2\sqrt{6}+3\right)+\left(2\sqrt{10}+2\sqrt{15}\right)+5}\)

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

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

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