Question

Answer 1

1: \(\sqrt{18}-2\sqrt{50}+3\sqrt8\)

\(=3\sqrt2-2\cdot5\sqrt2+3\cdot2\sqrt2\)

\(=3\sqrt2+6\sqrt2-10\sqrt2=-\sqrt2\)

2: \(\left(\sqrt7-\sqrt3\right)^2+\sqrt{84}\)

\(=7+3-2\cdot\sqrt{7\cdot3}+2\sqrt{21}\)

=7+3

=10

3: \(\left(\frac{6-2\sqrt2}{3-\sqrt2}-\frac{5}{\sqrt5}\right):\frac{1}{2-\sqrt5}\)

\(=\left(\frac{2\left(3-\sqrt2\right)}{3-\sqrt2}-\sqrt5\right)\left(2-\sqrt5\right)\)

\(=\left(2-\sqrt5\right)\left(2-\sqrt5\right)=\left(\sqrt5-2\right)^2=9-4\sqrt5\)