Question

√6-2√5

Answer 1

\(\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-1\right)^2}=\left|\sqrt{5}-1\right|=\sqrt{5}-1\)

Answer 2

\(\sqrt{6}-2\sqrt{5}=\sqrt{2}\cdot\sqrt{3}-2\sqrt{5}=\sqrt{2}\cdot\sqrt{3}-\sqrt{2}\cdot\sqrt{2}\cdot\sqrt{5}=\sqrt{2}\left(\sqrt{3}-\sqrt{2}\cdot\sqrt{5}\right)=\sqrt{2}\left(\sqrt{3}-\sqrt{10}\right)\)