Question

\(\sqrt{36+12\sqrt{5}}\)

Answer 1

\(\sqrt{36+12\sqrt{5}}\)

⇔\(\sqrt{36}+\sqrt{4.3\sqrt{5}}\)

⇔\(6+2\sqrt{3\sqrt{5}}\)

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

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

Answer 2

\(\sqrt{36+12\sqrt{5}}=\sqrt{30+2\sqrt{6.6.5}+6}=\sqrt{\left(\sqrt{30}+\sqrt{6}\right)^2}=\sqrt{30}+\sqrt{6}\)