Question

thực hiện phép tính:

1, \(\sqrt{5+2\sqrt{24}}-\sqrt{2}\)

2, \(\frac{3-2\sqrt{3}}{\sqrt{3}-2}\) 3, \(\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\)

4, \(\frac{1}{1-\sqrt{2}}-\frac{1}{1+\sqrt{2}}\) 5, \(\frac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\frac{3-\sqrt{3}}{\sqrt{3}}-\frac{4}{1-\sqrt{7}}\)

Answer 1

a/ \(\sqrt{5+\sqrt{24}}-\sqrt{2}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{2}=\left|\sqrt{3}+\sqrt{2}\right|-\sqrt{2}=\sqrt{3}+\sqrt{2}-\sqrt{2}=\sqrt{3}\)

b/ \(\frac{3-2\sqrt{3}}{\sqrt{3}-2}=\frac{\sqrt{3}\left(\sqrt{3}-2\right)}{\sqrt{3}-2}=\sqrt{3}\)

c/ \(\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}=\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}=-\sqrt{5}\)

d/ \(\frac{1}{1-\sqrt{2}}-\frac{1}{1+\sqrt{2}}=\frac{1+\sqrt{2}-1+\sqrt{2}}{\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}=\frac{2\sqrt{2}}{1-2}=-2\sqrt{2}\)