Question

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

Answer 1

$a). \sqrt{48} -2 \sqrt{3} (2-5 \sqrt{12})=4 \sqrt{3} -2 \sqrt{3} (2-5 \cdot 2 \sqrt{3} )= \\ =4 \sqrt{3} -2 \sqrt{3} (2-10 \sqrt{3} )=4 \sqrt{3} -4 \sqrt{3} +20 \cdot 3=60 \\ b).(3+ \sqrt{3} )(2+ \sqrt{3} )=6+3 \sqrt{3} +2 \sqrt{3} +3=9+5 \sqrt{3} \\ c).( \sqrt{6} + \sqrt{5} )^2-120= \sqrt{6} ^2+2 \cdot \sqrt{6} \cdot \sqrt{5} + \sqrt{5} ^2-120= \\ =6+2 \sqrt{30} +5-120=-109+2 \sqrt{30}$