Question

Resolva, sem usar calculadora.
$\sqrt{5} \times \sqrt{2} = \\ \sqrt[3]{5} \times \sqrt{2} = \\ \sqrt[3]{5 \sqrt{2} } = \\ \sqrt{5} + \sqrt{2} = \\ \sqrt[3]{5} + \sqrt{2} = \\ 5 \sqrt{5} \times \sqrt[3]{5 \sqrt{2} } =$
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Answer 1

$\boxed{\boxed{\mathsf{ \sqrt{5} \times \sqrt{2}=\sqrt{10}}}}$

$\boxed{\boxed{\mathsf{\sqrt[3]{5} \times \sqrt{2} =\sqrt[6]{{5}^{2}}.\sqrt[6]{{2}^{3}}=\sqrt[6]{200}}}}$

$\boxed{\boxed{\mathsf{\sqrt{5}+\sqrt{2}\,n\tilde{a}o\,simplifica}}}$

$\boxed{\boxed{\mathsf{ \sqrt[3]{5} +\sqrt{2}\,n\tilde{a}o\,simplifica}}}$

$5 \sqrt{5} \times \sqrt[3]{5 \sqrt{2} } \\ = \sqrt{ {5}^{2}.5} \times \sqrt[3]{ \sqrt{ {5}^{2}.2 } } \\ = \sqrt{75} . \sqrt[3]{ \sqrt{50} } \\ = \sqrt{75} \times \sqrt[6]{50}$

$\sqrt{75} \times \sqrt[6]{50} = \sqrt[6]{ {75}^{3} } \times \sqrt[6]{50} \\ = \sqrt[6]{ {75}^{3}.50 } \\ = \sqrt[6]{ {( {5}^{2}.3)}^{3} .50}$

$\sqrt[6]{{5}^{6}.{3}^{3}. 50}=5\sqrt[6]{1350}$