Question

Rút gọn biểu thức:

a) \(\left(5\sqrt{2}+2\sqrt{5}\right)\sqrt{5}-\sqrt{250}\) b) \(\left(\sqrt{3}+\sqrt{2}\right)^2+\left(\sqrt{3}-\sqrt{2}\right)^2\)

c) \(\dfrac{2}{\sqrt{5}-\sqrt{3}}+\dfrac{3}{\sqrt{6}+\sqrt{3}}\) d) \(\dfrac{\sqrt{x-1-2\sqrt{x-2}}}{\sqrt{x-2}-1}\)

Answer 1

a)

\(\left(5\sqrt{2}+2\sqrt{5}\right)\sqrt{5}-\sqrt{250}\)

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

\(=\sqrt{5}.2\sqrt{5}=10\)

b)

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

\(=5+2\sqrt{6}+5-2\sqrt{6}=10\)

c)

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

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

d)

\(\dfrac{\sqrt{x-1-2\sqrt{x-2}}}{\sqrt{x-2}-1}\)

\(=\dfrac{\left(\sqrt{x-2}-1\right)^2}{\sqrt{x-2}-1}=\sqrt{x-2}-1\)