Question

Tinh:

a)\(\sqrt{10+2\sqrt{14}}.\sqrt{10+2\sqrt{14}}\)

b)\(\sqrt{7+\sqrt{12}}-\sqrt{7-\sqrt{12}}\)

Answer 1

\(\sqrt{7+2\sqrt{3}}-\sqrt{7-2\sqrt{3}};\left(\sqrt{7+\sqrt{12}}-\sqrt{7-\sqrt{12}}\right)^2=7+\sqrt{12}-\sqrt{12}+7-2\sqrt{\left(7+\sqrt{12}\right)\left(7-\sqrt{12}\right)}=14-2\sqrt{37}\Rightarrow\sqrt{7+\sqrt{12}}-\sqrt{7-\sqrt{12}}=\sqrt{14-2\sqrt{37}}\)

Answer 2

a) \(\sqrt{10+2\sqrt{14}}\cdot\sqrt{10+2\sqrt{14}}\)

\(=\sqrt{\left(10+2\sqrt{14}\right)^2}\)

\(=10+2\sqrt{14}\)

b) \(\sqrt{7+\sqrt{12}}-\sqrt{7-\sqrt{12}}\)

\(=\sqrt{\left(\sqrt{7+\sqrt{12}}-\sqrt{7-\sqrt{12}}\right)^2}\)

\(=\sqrt{7+\sqrt{12}+7-\sqrt{12}-2\sqrt{\left(7+\sqrt{12}\right)\left(7-\sqrt{12}\right)}}\)

\(=\sqrt{14-2\sqrt{49-12}}\)

\(=\sqrt{14-2\sqrt{37}}\)