Question

trục căn thức ở mẫu

a)\(\frac{5}{\sqrt{10}}\)

b)\(\frac{1}{3\sqrt{20}}\)

c)\(\frac{2\sqrt{2}+2}{5\sqrt{2}}\)

d)\(\frac{\sqrt{21}-\sqrt{7}}{1-\sqrt{3}}\) 

e)\(\frac{3}{\sqrt{3}+1}\) 

f)\(\frac{2}{\sqrt{3}-1}\)

Answer 1

a.\(\frac{5}{\sqrt{10}}=\frac{5\sqrt{10}}{10}=\frac{\sqrt{10}}{2}\)

b. \(\frac{1}{3\sqrt{20}}=\frac{\sqrt{20}}{60}=\frac{2\sqrt{5}}{60}=\frac{\sqrt{5}}{30}\)

c. \(\frac{2\sqrt{2}+2}{5\sqrt{2}}=\frac{2\left(\sqrt{2}+1\right)}{5\sqrt{2}}=\frac{2\sqrt{2}\left(\sqrt{2}+1\right)}{10}=\frac{\sqrt{2}\left(\sqrt{2}+1\right)}{5}\)

 

Answer 2

d.\(\frac{\sqrt{21}-\sqrt{7}}{1-\sqrt{3}}=\frac{\sqrt{7}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}=\frac{-\sqrt{7}\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=-\sqrt{7}\)

e.\(\frac{3}{\sqrt{3}+1}=\frac{3\left(\sqrt{3}-1\right)}{3-1}=\frac{3\left(\sqrt{3}-1\right)}{2}\)

f.\(\frac{2}{\sqrt{3}-1}=\frac{2\left(\sqrt{3}+1\right)}{3-1}=\frac{2\left(\sqrt{3}+1\right)}{2}=\sqrt{3}+1\)