Question

Tính:

a) \(\sqrt{\sqrt{5}-2}-\sqrt{5\sqrt{5}+10}+\sqrt{4\sqrt{5}+8}\)

b) \(\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2\sqrt{2}+2}\)

Answer 1

a.

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

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

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

\(=\sqrt{\sqrt{5}-2}-\sqrt{\sqrt{5}-2}.1=0\)

b.

\(=\sqrt{\sqrt{2}-1}+\sqrt{\sqrt{2}+1}-\sqrt{2\left(\sqrt{2}+1\right)}\)

\(=\sqrt{\sqrt{2}-1}-\left(\sqrt{2}-1\right)\left(\sqrt{\sqrt{2}+1}\right)\)

\(=\sqrt{\sqrt{2}-1}-\sqrt{\sqrt{2}-1}.\sqrt{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}\)

\(=\sqrt{\sqrt{2}-1}-\sqrt{\sqrt{2}-1}=0\)