Respuesta :

[tex] \sqrt{200} - \sqrt{32} = \sqrt{2 \times 100} - \sqrt{2 \times 16} = 10 \sqrt{2} - 4 \sqrt{2} = 6 \sqrt{2} [/tex]
[tex]\bf \sqrt{200}-\sqrt{32}\quad \begin{cases} 200=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \qquad 2^2\cdot 2\cdot 5^2\\ \qquad (2\cdot 5)^2\cdot 2\\ \qquad (10)^2\cdot 2\\ 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2^2\cdot 2\\ \qquad (2\cdot 2)^2\cdot 2\\ \qquad (4)^2\cdot 2 \end{cases}\implies \sqrt{10^2\cdot 2}-\sqrt{4^2\cdot 2} \\\\\\ 10\sqrt{2}-4\sqrt{2}\implies 6\sqrt{2}\implies 6\cdot 2^{\frac{1}{2}}[/tex]

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