Question

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

D=\(\sqrt{8}+\sqrt{18}-\sqrt{32}\)

E=\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

F=\(2\sqrt{8}-\sqrt{50}+\sqrt{\left(\sqrt{2}+1\right)^2}\)

Answer 1

\(C=\sqrt{\sqrt{\left(5+2\right)^2}}-\sqrt{5}\\ =\sqrt{5+2}-\sqrt{5}=\sqrt{7}-\sqrt{5}\)

\(D=\sqrt{8}+\sqrt{18}-\sqrt{32}\\ =\sqrt{2}\left(\sqrt{4}+\sqrt{9}-\sqrt{16}\right)\\ =\sqrt{2}\left(2+3-4\right)\\ =\sqrt{2}\)

\(E=\sqrt{9-4\sqrt{5}}-\sqrt{5}\\ =\sqrt{4+5-4\sqrt{5}}-\sqrt{5}\\ =\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\\ =\sqrt{5}-2-\sqrt{5}\\ =-2\)

\(F=2\sqrt{8}-\sqrt{50}+\sqrt{\left(\sqrt{2}+1\right)^2}\\ =2\sqrt{8}-\sqrt{50}+\sqrt{2}+1\\ =\sqrt{2}\left(2\sqrt{4}-\sqrt{25}+1\right)+1\\ =\sqrt{2}\left(4-5+1\right)+1=1\)