Question

4√12+5√27-6√48++√192-√363
(√2+1)²-2(√2+1)(√2-1)+(√2-2)²

Answer 1

4√12+5√27-6√48+√192-√363=
4*2√3+5*3√3-6*4√3+8√3-11√3=-4√3
(√2+1)²-2(√2+1)(√2-1)+(√2-2)²=(√2)²+2√2+1-2[(√2)²-1]+(√2)²-4√2+4=2+2√2+1-2*2+2+2-4√2+4=2+2√2+1-4+2+2-4√2+4=7-2√2

Answer 2

$a).4 \sqrt{12} +5 \sqrt{27} -6 \sqrt{48} + \sqrt{192} - \sqrt{363} = \\ =4 \cdot 2 \sqrt{3} +5 \cdot 3 \sqrt{3} -6 \cdot 4 \sqrt{3} +8 \sqrt{3} -11 \sqrt{3} = \\ =8 \sqrt{3} +15 \sqrt{3} -24 \sqrt{3} +8 \sqrt{3} -11 \sqrt{3} =-4 \sqrt{3}$
$b).( \sqrt{2} +1)^2-2( \sqrt{2} +1)( \sqrt{2} -1)+( \sqrt{2} -2)^2= \\ =( \sqrt{2} )^2+2\cdot \sqrt{2} \cdot 1+1^2-2(2-1)+( \sqrt{2} )^2-2 \cdot \sqrt{2} \cdot 2+2^2= \\ =2+2 \sqrt{2} +1-2 \cdot 1+2-4 \sqrt{2} +4= \\ =2+2 \sqrt{2} +1-2 +2-4 \sqrt{2} +4=7-2 \sqrt{2}$