Question

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

Answer 1

C=\(\left(\sqrt{10}-\sqrt{2}\right).\sqrt{3+\sqrt{5}}=\sqrt{2}\left(\sqrt{5}-1\right).\sqrt{3+\sqrt{5}}=\left(\sqrt{5}-1\right).\sqrt{2}.\sqrt{3+\sqrt{5}}=\left(\sqrt{5}-1\right).\sqrt{2\left(3+\sqrt{5}\right)}=\left(\sqrt{5}-1\right)\sqrt{6+2\sqrt{5}}=\left(\sqrt{5}-1\right).\sqrt{5+2\sqrt{5}+1}=\left(\sqrt{5}-1\right)\sqrt{\left(\sqrt{5}+1\right)^2}=\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)=\left(\sqrt{5}\right)^2-1^2=5-1=4\)