Question

Trục căn thức ở mẫu các biểu thức sau:

a) \(\frac{{\sqrt 7 }}{{\sqrt 3 }}\)

b) \( - \frac{{10}}{{3\sqrt 5 }}\)

c) \(\frac{{2\sqrt 2 }}{{\sqrt {40} }}\)

d) \(\frac{{\sqrt 2 }}{{\sqrt 5  - \sqrt 2 }}\)

Answer 1

a) \(\frac{{\sqrt 7 }}{{\sqrt 3 }} = \frac{{\sqrt 7 .\sqrt 3 }}{{\sqrt 3 .\sqrt 3 }} = \frac{{\sqrt {21} }}{3}\)

b) \( - \frac{{10}}{{3\sqrt 5 }} =  - \frac{{10.\sqrt 5 }}{{3\sqrt 5 .\sqrt 5 }} =  - \frac{{10\sqrt 5 }}{{15}}\)

c) \(\frac{{2\sqrt 2 }}{{\sqrt {40} }} = \frac{{2\sqrt 2 .\sqrt {40} }}{{\sqrt {40} .\sqrt {40} }} = \frac{{8\sqrt 5 }}{{40}} = \frac{{\sqrt 5 }}{5}\)

d) \(\frac{{\sqrt 2 }}{{\sqrt 5  - \sqrt 2 }}\) \( = \frac{\sqrt 2 .\left( {\sqrt 5  + \sqrt 2 } \right)}{\left( {\sqrt 5  - \sqrt 2 } \right).\left( {\sqrt 5  + \sqrt 2 } \right)}\) \( = \frac{\sqrt 2 .\sqrt 5  + \sqrt 2.\sqrt 2 }{{\left( {\sqrt 5 } \right)}^2 - {\left( {\sqrt 2 } \right)^2}}\) \( = \frac{{\sqrt 10  + 2 }}{{5 - 2}}\) \( = \frac{{\sqrt 10  + 2}}{3}\)