Question

1. Tính

a) \(\frac{3-\sqrt{3}}{\sqrt{3}}\)

b)\(\frac{2\sqrt{2}+\sqrt{6}}{4+\sqrt{12}}\)

c)\(\frac{1-\sqrt{a^3}}{a-1}\)

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

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

2. Rút gọn

\(\frac{1}{\sqrt{1}+1}-\frac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\)

Answer 1

a)\(\frac{3-\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}\left(\sqrt{3}-1\right)}{\sqrt{3}}=\sqrt{3}-1\)

b)\(\frac{2\sqrt{2}+\sqrt{6}}{4+\sqrt{12}}=\frac{\sqrt{2}\left(2+\sqrt{3}\right)}{2\left(2+\sqrt{3}\right)}=\frac{\sqrt{2}}{2}\)

c)\(\frac{1-\sqrt{a^3}}{a-1}=\frac{1-\sqrt{a}^3}{-\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}=\frac{-\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}=\frac{-1-\sqrt{a}-a}{1+\sqrt{a}}\)

d)\(\frac{\sqrt{6+2\sqrt{5}}}{\sqrt{5}+1}=\frac{\sqrt{5+2\sqrt{5}+1}}{\sqrt{5}+1}=\frac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{5}+1}=\frac{\left|\sqrt{5}+1\right|}{\sqrt{5}+1}=\frac{\sqrt{5}+1}{\sqrt{5}+1}=1\)

e)\(\frac{\sqrt{5+2\sqrt{6}}}{\sqrt{3}+\sqrt{2}}=\frac{\sqrt{3+2\sqrt{6}+2}}{\sqrt{3}+\sqrt{2}}=\frac{\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}}{\sqrt{3}+\sqrt{2}}=\frac{\left|\sqrt{3}+\sqrt{2}\right|}{\sqrt{3}+\sqrt{2}}=1\)

Answer 2

Yến Nhi Phạm Trần câu 2 sai đề hay sao í số xấu lắm