Question

Rút gọn các biểu thức sau:

a) \(\sqrt {20}  - \sqrt 5 \)

b) \(\sqrt {32}  - \sqrt {18}  + \frac{4}{{\sqrt 2 }}\)

c) \(\left( {2 - \sqrt {10} } \right)\left( {\sqrt 2 - \sqrt 5 } \right)\)

Answer 1

a) \(\sqrt {20}  - \sqrt 5  = \sqrt {{2^2}.5}  - \sqrt 5  = 2\sqrt 5  - \sqrt 5  = \sqrt 5 \)

b) \(\sqrt {32}  - \sqrt {18}  + \frac{4}{{\sqrt 2 }}\)\( = \sqrt {16.2}  - \sqrt {9.2}  + \frac{4\sqrt 2}{{2 }}\)\( = 4\sqrt 2  - 3\sqrt 2  + 2\sqrt 2\)\( = 3\sqrt 2\)

c) \(\left( {2 - \sqrt {10} } \right)\left( {\sqrt 2 - \sqrt 5 } \right)\)\( = 2\sqrt 2 - 2\sqrt 5  - \sqrt {10}.\sqrt 2  + \sqrt {10} .\sqrt 5 \)\( = 2\sqrt 2 - 2\sqrt 5  - \sqrt {20} + \sqrt {50}\)\( = 2\sqrt 2 - 2\sqrt 5  - 2\sqrt 5 + 5\sqrt 2\)\( = \left(2\sqrt 2 + 5\sqrt 2 \right) - \left(2\sqrt 5  + 2\sqrt 5\right)\)\( = 7\sqrt 2 - 4\sqrt 5\)