Question

Rút gọn biểu thức:

a)\(\dfrac{\sqrt{8}+2}{\sqrt{2}+1}.\sqrt{2}\)

b) \(\dfrac{5+\sqrt{5}}{\sqrt{5}+1}.\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)

c)\(\dfrac{2}{\sqrt{2}}+\sqrt{18}-\sqrt{32}\)

d) \(\left(1-\dfrac{2+\sqrt{2}}{\sqrt{2}+1}\right)\left(1+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\right)\)

Answer 1

\(a.\dfrac{\sqrt{8}+2}{\sqrt{2}+1}.\sqrt{2}=\dfrac{\sqrt{2}.2\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=2\sqrt{2}\)

\(b.\dfrac{5+\sqrt{5}}{\sqrt{5}+1}.\dfrac{5-\sqrt{5}}{\sqrt{5}-1}=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}+1}.\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}=\sqrt{5}.\sqrt{5}=5\)

\(c.\dfrac{2}{\sqrt{2}}+\sqrt{18}+\sqrt{32}=\sqrt{2}+\sqrt{9.2}+\sqrt{16.2}=\sqrt{2}+3\sqrt{2}+4\sqrt{2}=8\sqrt{2}\)

\(d.\left(1-\dfrac{2+\sqrt{2}}{\sqrt{2}+1}\right)\left(1+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\right)=\left(1-\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\right)\left(1+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\right)=\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)=1-2=-1\)

Answer 2