Question

Answer 1

\(a,\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\\ =\sqrt{\left(9-\sqrt{17}\right)\left(9+\sqrt{17}\right)}\\ =\sqrt{81-17}=\sqrt{64}=8\)

\(b,2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\\ =2\sqrt{6}-4\sqrt{2}+9+4\sqrt{2}-2\sqrt{6}\\ =9\)

Answer 2

a: \(\sqrt{9-\sqrt{17}}\cdot\sqrt{9+\sqrt{17}}\)

\(=\sqrt{81-17}\)

=8

b: \(2\sqrt{2}\left(\sqrt{3}-2\right)+\left(1+2\sqrt{2}\right)^2-2\sqrt{6}\)

\(=2\sqrt{6}-4\sqrt{2}+9+4\sqrt{2}-2\sqrt{6}\)

=9