Question

√(10-2√6-2√10+2√15)

Answer 1

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

\(=\sqrt{\left(\sqrt{2}\right)^2+\left(\sqrt{3}\right)^2+\left(\sqrt{5}\right)^2-2\sqrt{2.3}-2\sqrt{2.5}+2\sqrt{3.5}}\)

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

\(=\sqrt{3}+\sqrt{5}-\sqrt{2}\)
\(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ac\)

Answer 2

\(=\sqrt{10-2\cdot\sqrt{2}\cdot\sqrt{3}-2\cdot\sqrt{2}\cdot\sqrt{5}+2\cdot\sqrt{3}\cdot\sqrt{5}}\)

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

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