Question

Tính

a) \(\left( {\sqrt {\frac{4}{3}}  + \sqrt 3 } \right)\sqrt 6 \)

b) \(\sqrt {18} :\sqrt 6  + \sqrt 8 .\sqrt {\frac{{27}}{2}} \)

c) \({\left( {1 - 2\sqrt 5 } \right)^2}\)

Answer 1

a) \(\left( {\sqrt {\frac{4}{3}}  + \sqrt 3 } \right)\sqrt 6  = \sqrt {\frac{4}{3}} .\sqrt 6  + \sqrt 3 .\sqrt 6  \) \(= \sqrt {\frac{{24}}{3}}  + \sqrt {18} \)\(=\sqrt 8  + \sqrt {18}  \)\(= \sqrt {2.4}  + \sqrt {2.9}  \)\(= 2\sqrt 2  + 3\sqrt 2  \)\(= 5\sqrt 2 \)

b) \(\sqrt {18} :\sqrt 6  + \sqrt 8 .\sqrt {\frac{{27}}{2}} \)\( = \sqrt {\frac{{18}}{6}}  + \sqrt {8.\frac{{27}}{2}} \)\( = \sqrt 3  + \sqrt {108} \)\( = \sqrt 3  + \sqrt {36.3} \)\( = \sqrt 3  + 6\sqrt 3 \)\( = 7\sqrt 3 \)

c) \({\left( {1 - 2\sqrt 5 } \right)^2} = 1 - 4\sqrt 5  + 20 = 21 - 4\sqrt 5 \)