Question

1) \(\sqrt{28+10\sqrt{3}}-\sqrt{28-10\sqrt{3}}\)

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

Answer 1

1)

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

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

= \(2\sqrt{3}\)

2:

BT = \(\frac{\sqrt{2}.\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}-\frac{5\left(\sqrt{6}-1\right)}{\left(1+\sqrt{6}\right)\left(\sqrt{6}-1\right)}\)

= \(\sqrt{6}-\frac{5\left(\sqrt{6}-1\right)}{5}\) = \(\sqrt{6}-\left(\sqrt{6}-1\right)\) =1