Question

Rút gọn

a,\(\sqrt{227-30\sqrt{2}}\) + \(\sqrt{123+22\sqrt{2}}\)

b,\(\dfrac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)

c, \(\sqrt{2-\sqrt{3}}\) (\(\sqrt{5}\) + \(\sqrt{2}\))

Answer 1

a)

=\(\sqrt{15^2-2\cdot15\cdot\sqrt{2}+2}+\sqrt{11^2+2\cdot11\cdot\sqrt{2}+2}\)

=\(\sqrt{\left(15-\sqrt{2}\right)^2}+\sqrt{\left(11+\sqrt{2}\right)}^2\)

=\(15-\sqrt{2}+11+\sqrt{2}\)

=26

c)

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

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