Question

Answer 1

a) \(\sqrt{\left(\sqrt{17}-4\right)^2}=\sqrt{17}-4\)

b, \(\sqrt{\left(5-\sqrt{6}\right)^2}-\sqrt{\left(2-\sqrt{6}\right)^2}=5-\sqrt{6}-\sqrt{6}+2=7-2\sqrt{6}\)

Answer 2

a) \(\sqrt{\left(\sqrt{17}-4\right)^2}=\left|\sqrt{17}-4\right|=\sqrt{17}-4\)

b) \(\sqrt{\left(5-\sqrt{6}\right)^2}-\sqrt{\left(2-\sqrt{6}\right)^2}=\left|5-\sqrt{6}\right|-\left|2-\sqrt{6}\right|=5-\sqrt{6}+2-\sqrt{6}=7-2\sqrt{6}\)

c) \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}=\left|\sqrt{5}-\sqrt{2}\right|-\left|\sqrt{5}+\sqrt{2}\right|=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)

Answer 3

a: \(\sqrt{\left(\sqrt{17}-4\right)^2}=\sqrt{17}-4\)

b: \(\sqrt{\left(5-\sqrt{6}\right)^2}-\sqrt{\left(2-\sqrt{6}\right)^2}\)

\(=5-\sqrt{6}-\sqrt{6}+2\)

\(=7-2\sqrt{6}\)

c: \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

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

\(=-2\sqrt{2}\)