Question

de adus la forma cea mai simpla expresia√ (√2-4)² +√(√7+2√2)²-√(3-2√7)²

Answer 1

$\displaystyle \sqrt{\left( \sqrt{2}-4\right)^2 } + \sqrt{\left( \sqrt{7}+2 \sqrt{2}\right)^2 } - \sqrt{\left(3-2 \sqrt{7}\right)^2 } = \\ \\ =\left| \sqrt{2} -4\right|+\left| \sqrt{7} +2 \sqrt{2} \right|-\left|3-2 \sqrt{7} \right|= \\ \\ =4- \sqrt{2} +2 \sqrt{2} + \sqrt{7} -\left(2 \sqrt{7} -3\right)= \\ \\ =4- \sqrt{2} +2 \sqrt{2} + \sqrt{7} -2 \sqrt{7} +3=7+ \sqrt{2} - \sqrt{7}$