Question

aduceti la forma cea mai simpla √3(√12-2√27)
√48-2√3(2-5√12)
(3+√3)(2+√3)
(√6+√5)²-√120

Answer 1

$\sqrt{3} ( \sqrt{12} -2 \sqrt{27} )= \sqrt{3} (2 \sqrt{3} -2 \cdot 3 \sqrt{3})= \sqrt{3} (2 \sqrt{3} -6 \sqrt{3} )= \\ = \sqrt{3} \cdot (-4 \sqrt{3} )=-4 \cdot 3=-12 \\ \\ \sqrt{48} -2 \sqrt{3} (2-5 \sqrt{12} )=4 \sqrt{3} -2 \sqrt{3} (2-5 \cdot 2 \sqrt{3} )= \\ =4 \sqrt{3} -2 \sqrt{3} (2-10 \sqrt{3} )=4 \sqrt{3} -4 \sqrt{3} +20 \cdot 3=60 \\ \\ (3+ \sqrt{3} )(2+ \sqrt{3} )=6+3 \sqrt{3} +2 \sqrt{3} +3=9+5 \sqrt{3}$

$( \sqrt{6} + \sqrt{5} )^2- \sqrt{120} = \sqrt{6} ^2+2 \cdot \sqrt{6} \cdot \sqrt{5} + \sqrt{5} ^2-2 \sqrt{30} = \\ =6+2 \sqrt{30} +5-2 \sqrt{30} =6+5=11$