Question

Aduceți la formă mai simplă expresia:
√(3√3-2)^2+2|√13-3|-7,5(4-√8)^2+6,4:(5-1,8)=

Answer 1

√(3√3-2)^2+2|√13-3|-7,5(4-√8)^2+6,4:(5-1,8)=

$\it n=\sqrt{(3\sqrt3-2)^2}+2|\sqrt3-3|-7,5(4-\sqrt8)^2+6,4:(5-1,8)\\ \\ 3\sqrt3-2 > 0 \Rightarrow \sqrt{(3\sqrt3-2)^2} =3\sqrt3-2\\ \\ \sqrt3-3 < 0 \Rightarrow 2|\sqrt3-3|=2(-\sqrt3+3)=-2 \sqrt3+6\\ \\ 7,5(4-8^2)^2=7,5(16-8\sqrt8+8)=7,5\cdot(24-16\sqrt2)=180-120\sqrt2\\ \\ 6,4:(5-1,8)=6,4:3,2=64:32=2$

$\it n=3\sqrt3-\not2-2\sqrt3+6-180+120\sqrt2+\not2=-174+120\sqrt2+\sqrt3$