Question

Sa se aduca la o forma mai simpla expresiile :
a) radical din 12 +2 radical din 27 + radical din 3 radical 75 - 9 radical din 48 + radical din 192 - 8 radical din 3
b) vezi imagininea
c) vezi imagininea

Answer 1

$a) \sqrt{12} + 2 \sqrt{27} + \sqrt{3} \times \sqrt{75} - 9 \sqrt{48} + \sqrt{192} - 9 \sqrt{3}$

$= 2 \sqrt{3} + 2 \times 3 \sqrt{3} + \sqrt{3} \times 5 \sqrt{3} - 9 \times 4 \sqrt{3} + 8 \sqrt{3} - 9 \sqrt{3}$

$= 2 \sqrt{3} + 6 \sqrt{3} + 5 \sqrt{9} - 36 \sqrt{3} + 8 \sqrt{3} - 9 \sqrt{3}$

$= 8 \sqrt{3} + 5 \times 3 - 37 \sqrt{3}$

$= - 29 \sqrt{3} + 15$

$b)(2 \sqrt{3} - 3 \sqrt{2} + \sqrt{6} )( \sqrt{6} - \sqrt{2} - 2 \sqrt{3} )$

$= 2 \sqrt{3} \times \sqrt{6} + 2 \sqrt{3} \times ( - \sqrt{2} ) + 2 \sqrt{3} \times ( - 2 \sqrt{3} ) - 3 \sqrt{2} \times \sqrt{6} - 3 \sqrt{2} \times ( - \sqrt{2} ) - 3 \sqrt{2} \times ( - 2 \sqrt{3} ) + \sqrt{6} \times \sqrt{6} + \sqrt{6} \times ( - \sqrt{2} ) + \sqrt{6} \times ( - 2 \sqrt{3} )$

$= 2 \sqrt{18} - 2 \sqrt{6} - 4 \sqrt{9} - 3 \sqrt{12} + 3 \sqrt{4} + 6 \sqrt{6} + \sqrt{36} - \sqrt{12} - 2 \sqrt{18}$

$= - 2 \sqrt{6} - 4 \times 3 - 3 \times 2 \sqrt{3} + 3 \times 2 + 6 \sqrt{6} + 6 - 2 \sqrt{3}$

$= - 2 \sqrt{6} - 12 - 6 \sqrt{3} + 6 + 6 \sqrt{6} + 6 - 2 \sqrt{3}$

$= 4 \sqrt{6} - 8 \sqrt{3}$

$c) \frac{ \sqrt{2} }{ \sqrt{18} } + \frac{ \sqrt{7} }{ \sqrt{28} } - \frac{ \sqrt{11} }{ \sqrt{99} }$

$= \sqrt{ \frac{2}{18} } + \sqrt{ \frac{7}{28} } - \sqrt{ \frac{11}{99} }$

$= \sqrt{ \frac{1}{9} } + \sqrt{ \frac{1}{4} } - \sqrt{ \frac{1}{9} }$

$= \sqrt{ \frac{1}{4} }$

$= \frac{ \sqrt{1} }{ \sqrt{4} }$

$= \frac{1}{2}$