Question

Tính :

1)\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)

2)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)

3)\(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right).\sqrt{\sqrt{3}+2}\)

4)\(\left(5+\sqrt{21}\right).\left(\sqrt{14}-\sqrt{6}\right).\sqrt{5-\sqrt{21}}\)

Answer 1

a)\(\left(\sqrt{21}+7\right)\cdot\sqrt{10-2\sqrt{21}}\)

\(=\left(\sqrt{21}+7\right)\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)

\(=\sqrt{7}\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{7}-\sqrt{3}\right)\)

\(=\sqrt{7}\left(7-3\right)=4\sqrt{7}\)

b)\(\left(7+\sqrt{14}\right)\sqrt{9-2\sqrt{14}}\)

\(=\left(7+\sqrt{14}\right)\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)

\(=\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)\)

\(=\sqrt{7}\left(7-2\right)=5\sqrt{7}\)