Question

qual o valor da expressão (5√8 - 2√2) ³ ????

Answer 1

$\sqrt{8}=\sqrt{4\cdot2}\\\sqrt{8}=\sqrt{4}\cdot\sqrt{2}\\\sqrt{8}=2\cdot\sqrt{2}\\\sqrt{8}=2\sqrt{2}$
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$(5\sqrt{8}-2\sqrt{2})^{3}=(5\cdot2\sqrt{2}-2\sqrt{2})\\(5\sqrt{8}-2\sqrt{2})^{3}=(10\sqrt{2}-2\sqrt{2})^{3}\\(5\sqrt{8}-2\sqrt{2})^{3}=(8\sqrt{2})^{3}\\(5\sqrt{8}-2\sqrt{2})^{3}=8^{3}\sqrt{2^{3}}\\(5\sqrt{8}-2\sqrt{2})^{3}=512\sqrt{2^{2}}\cdot\sqrt{2}\\(5\sqrt{8}-2\sqrt{2})^{3}=512\cdot2\cdot\sqrt{2}\\\\\boxed{\boxed{(5\sqrt{8}-2\sqrt{2})^{3}=1024\sqrt{2}}}$

Answer 2

$x=(5 \sqrt{8}-2 \sqrt{2})^3 \\ x=(5 \sqrt{2.2.2}-2 \sqrt{2})^3 \\ x=(5 \sqrt{2^2.2}-2 \sqrt{2})^3 \\ x=(5.2\sqrt{2}-2 \sqrt{2})^3 \\ x=(10\sqrt{2}-2 \sqrt{2})^3 \\ x=(8\sqrt{2})^3 \\ x=8^3\sqrt{2^3} \\ x=8.8.8\sqrt{2^2.2} \\ x=64.8.2\sqrt{2} \\ x=512.2\sqrt{2} \\ \boxed {x=1024\sqrt{2}}$