Question

Rút gọn biểu thức

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

2)\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

3)\(\left(\sqrt{9-2\sqrt{14}}+\dfrac{5}{\sqrt{7}-\sqrt{2}}\right)^2\)

Answer 1

1: \(=\sqrt{4-2\sqrt{3}}\cdot\left(\sqrt{3}+1\right)\left(2+\sqrt{3}\right)\)

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

\(=2\left(2+\sqrt{3}\right)=4+2\sqrt{3}\)

2: \(=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)

\(=\sqrt{6+2\left(\sqrt{3}-1\right)}\)

\(=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)

3: \(=\left(\sqrt{7}-\sqrt{2}+\sqrt{7}+\sqrt{2}\right)^2=\left(2\sqrt{7}\right)^2=28\)