Question

Determine o Valor da soma:  $\sqrt{32} + 4 \sqrt{8} - ( \sqrt{2} ) ^{2}$

Qual é o resultado de $( \sqrt{5} - \sqrt{2}) ( \sqrt{2} + \sqrt{5} )$

Alguém poderia me passar o resultado e a solução dessas contas?

Ignores aquele A na segunda questão

Answer 1

$1.a)\ \sqrt{32}+4\sqrt{8}-(\sqrt{2})^2\\\\ \sqrt{2^2 \times 2^2 \times 2}+4\sqrt{2^2 \times 2}-(\not\sqrt{2})^{\not2}\\\\ (2\times 2)\sqrt{2}+(4 \times 2)\sqrt{2}-2\\\\ 4\sqrt{2}+8\sqrt{2}-2\\\\ \boxed{12\sqrt{2}-2}\ \ \ ou\ \ \ \boxed{2(6\sqrt{2}-1)}$

$1.b)\ \sqrt{32}+4\sqrt{8}-(\sqrt{2})^3\\\\ =\sqrt{2^2 \times 2^2 \times 2}+4\sqrt{2^2 \times 2}-(\sqrt{2^3})\\\\ =\sqrt{2^2 \times 2^2 \times 2}+4\sqrt{2^2 \times 2}-(\sqrt{2^2 \times 2})\\\\ =(2\times 2)\sqrt{2}+(4 \times 2)\sqrt{2}-2\sqrt{2}\\\\ =4\sqrt{2}+8\sqrt{2}-2\sqrt{2}\\\\ \boxed{=10\sqrt{2}}$

$2) (\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})\\\\ = (\sqrt{5} \times \sqrt{2})+(\sqrt{5} \times \sqrt{5})-(\sqrt{2} \times \sqrt{2})-(\sqrt{2} \times \sqrt{5})\\\\ = (\sqrt{5 \times 2})+(\sqrt{5 \times 5})-(\sqrt{2 \times 2})-(\sqrt{2 \times 5})\\\\ = (\sqrt{10})+(\sqrt{5^2})-(\sqrt{2^2})-(\sqrt{10})\\\\ = (\sqrt{10})+(\not\sqrt{5^{\not2}})-(\not\sqrt{2^{\not2}})-(\sqrt{10})\\\\ = \sqrt{10}+5-2-\sqrt{10}\\\\ = \not\sqrt{\not10}-\not\sqrt{\not10}+5-2\\\\ \boxed{=3}$

Espero ter ajudado.
Bons estudos!