Question

Answer 1

\(M=\sqrt{\sqrt{17}-4}.\sqrt{\sqrt{17}+4}\)

\(=\sqrt{17-16}\)

\(=\sqrt{1}=1\)

Answer 2

\(N=\sqrt{\left(\sqrt{5}-2\right)^2}-\dfrac{1}{\sqrt{5}-2}\)

\(=\sqrt{5}-2-\dfrac{1}{\sqrt{5}-2}\)

\(=\dfrac{\left(\sqrt{5}-2\right)^2-1}{\sqrt{5}-2}\)

\(=\dfrac{8-4\sqrt{5}}{\sqrt{5}-2}\)

\(=-\dfrac{4\left(\sqrt{5}-2\right)}{\sqrt{5}-2}=-4\)