Question

Trục căn ở mẫu:

a, \(\frac{9}{\sqrt{3}}\)

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

c, \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)

d, \(\frac{1}{\sqrt{18}+\sqrt{8}-2\sqrt{2}}\)

Answer 1

a) \(\frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=3\sqrt{3}\)

b) \(\frac{3}{\sqrt{5}-\sqrt{2}}=\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}=\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{5-2}=\sqrt{5}+\sqrt{2}\)

c) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\frac{\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\frac{5-2\sqrt{15}+3}{5-3}=\frac{8-2\sqrt{15}}{2}=4-\sqrt{15}\)

d) \(\frac{1}{\sqrt{18}+\sqrt{8}-2\sqrt{2}}=\frac{1}{3\sqrt{2}+2\sqrt{2}-2\sqrt{2}}=\frac{1}{3\sqrt{2}}=\frac{\sqrt{2}}{3\sqrt{2}\cdot\sqrt{2}}=\frac{\sqrt{2}}{6}\)