Question

rút gọn các biểu thức sau

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

b)\(\frac{2-\sqrt{2}}{\sqrt{2}}\)

c)\(\frac{x-y+3\sqrt{x}+3\sqrt{y}}{\sqrt{x}-\sqrt{y}+3}\)

 

Answer 1

a. \(\left(\sqrt{5-2\sqrt{6}}+\sqrt{2}\right).\sqrt{3}=\left(\left|\sqrt{3}-\sqrt{2}\right|+\sqrt{2}\right).\sqrt{3}=\left(\sqrt{3}\right)^2=3\)

Answer 2

b.\(\frac{2-\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}\left(2-\sqrt{2}\right)}{2}=\frac{2\sqrt{2}-2}{2}=\frac{2\left(\sqrt{2}-1\right)}{2}=\sqrt{2}-1\)

Answer 3

\(\frac{x-y+3\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}+3}=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)+3\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}+3}=\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}+3\right)}{\sqrt{x}-\sqrt{y}+3}=\sqrt{x}+\sqrt{y}\)