Question

Tính:

M = \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\times\sqrt{2}+\sqrt{20}\)

N = \(\left(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}\right):\dfrac{1}{\sqrt{5}-\sqrt{2}}\)

Answer 1

M = \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\times\sqrt{2}+\sqrt{20}\)

= \(2-\sqrt{6-2\sqrt{5}}+\sqrt{20}\)

= \(2-\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{20}\)

= 2 \(-\sqrt{5}+1+\sqrt{20}\)

= 3 + \(\sqrt{5}\)

Answer 2

\(M=\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\sqrt{2}+\sqrt{20}=2-\sqrt{5-2\sqrt{5}+1}+\sqrt{20}=2-\sqrt{5}-1+2\sqrt{5}=1+\sqrt{5}\) \(N=\left(\dfrac{\sqrt{6}-\sqrt{2}}{1-\sqrt{3}}-\dfrac{5}{\sqrt{5}}\right):\dfrac{1}{\sqrt{5}-\sqrt{2}}=-\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{2}\right)=-\left(5-2\right)=-3\)