Question

(√2 -√8)² / (1 - √7)(1 + √7)

Answer 1

(√2 -√8).(√2 -√8) / (1 - √7).(1 + √7)

2-√16-√16+8
      1-7
2-8+8
 -6
=-1/3

Answer 2

$\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2*\sqrt{2}=2\sqrt{2}$

Lembre-se do produto da soma pela diferença de 2 termos:

$(a+b)(a-b)\rightleftharpoons a^{2}-b^{2}$
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$\dfrac{(\sqrt{2}-\sqrt{8})^{2}}{(1-\sqrt{7})(1+\sqrt{7})}=\dfrac{(\sqrt{2}-2\sqrt{2})^{2}}{1^{2}-(\sqrt{7})^{2}}\\\\\\\dfrac{(\sqrt{2}-\sqrt{8})^{2}}{(1-\sqrt{7})(1+\sqrt{7})}=\dfrac{(-\sqrt{2})^{2}}{1-7}\\\\\\\dfrac{(\sqrt{2}-\sqrt{8})^{2}}{(1-\sqrt{7})(1+\sqrt{7})}=\dfrac{2}{-6}\\\\\\\boxed{\boxed{\frac{(\sqrt{2}-\sqrt{8})^{2}}{(1-\sqrt{7})(1+\sqrt{7})}=-\dfrac{1}{3}}}$