Question

\(B=\sqrt{28-16\sqrt{3}}\)

\(C=\sqrt{4+\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)\)

Answer 1

B=\(\sqrt{28-16\sqrt{3}}=\sqrt{16-2.4.2\sqrt{3}+12}\sqrt{4^2-2.4.2\sqrt{3}+\left(2\sqrt{3}\right)^2}=\sqrt{\left(4-2\sqrt{3}\right)^2}=\left|4-2\sqrt{3}\right|=4-2\sqrt{3}\)C=\(\sqrt{4+\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)=\sqrt{4+\sqrt{15}}.\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)=\sqrt{2\left(4+\sqrt{15}\right)}\left(\sqrt{5}-\sqrt{3}\right)=\sqrt{8+2\sqrt{15}}\left(\sqrt{5}-\sqrt{3}\right)=\sqrt{3+2.\sqrt{3}.\sqrt{5}+5}\left(\sqrt{5}-\sqrt{3}\right)=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\left(\sqrt{5}-\sqrt{3}\right)=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)