Question

[hsrhsrhjs]

1/\(\frac{4\sqrt{2}}{2+\sqrt{2}}-\frac{4\sqrt{2}}{2-\sqrt{2}}\)

2/ \(\frac{2}{\sqrt{2}}+\sqrt{2}-2\sqrt{18}+\sqrt{\left(1-\sqrt{2}\right)^2}\)

3/ \(9\sqrt{\frac{2}{3}}+5\sqrt{54}-\sqrt{\frac{1}{2}-\frac{1}{3}}\)

4/ \(\sqrt{4+2\sqrt{2}}.\sqrt{4-2\sqrt{2}}.\left(\sqrt{8}-\sqrt{2}\right)\)

5/ \(\sqrt{14-6\sqrt{5}}+\sqrt{3-2\sqrt{2}}+\sqrt{7-2\sqrt{10}}\)

Answer 1

[Vũ Hoàng]

1, \(=\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2^2-\sqrt{2}^2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2^2-\sqrt{2}^2}\)

=\(\frac{4\sqrt{2}\left(2-\sqrt{2}\right)}{2}-\frac{4\sqrt{2}\left(2+\sqrt{2}\right)}{2}\)

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

=\(4\sqrt{2}-4-4\sqrt{2}-4\)

=-8

2, =\(\sqrt{2}+\sqrt{2}-2.3\sqrt{2}+\left|1-\sqrt{2}\right|\)

= \(-4\sqrt{2}+1-\sqrt{2}\) = \(1-5\sqrt{2}\)

3, =\(9\sqrt{\frac{2.2}{3.2}}+5\sqrt{9.6}-\sqrt{\frac{1}{6}}\)

=\(3\sqrt{6}+15\sqrt{6}-\frac{1}{6}\sqrt{6}\)

=\(\frac{107}{6}\sqrt{6}\)

4, =\(\sqrt{\left(4+2\sqrt{2}\right)\left(4-2\sqrt{2}\right)}.\left(2\sqrt{2}-\sqrt{2}\right)\)

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

= \(\sqrt{16-8}.\sqrt{2}\)

= \(\sqrt{8}.\sqrt{2}=\sqrt{16}=4\)

5, = \(\sqrt{9-2.3.\sqrt{5}+5}+\sqrt{1-2.1.\sqrt{2}+2}+\sqrt{5-2.\sqrt{2}.\sqrt{5}+2}\)

\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{(1-\sqrt{2})^2}+\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}\)\(=\left|3-\sqrt{5}\right|+\left|1-\sqrt{2}\right|+\left|\sqrt{5}-\sqrt{2}\right|\)

\(=3-\sqrt{5}+1-\sqrt{2}+\sqrt{5}-\sqrt{2}\)

\(=4-2\sqrt{2}\)