прошу хелп [tex]\sqrt[5]{1\frac{11}{16}* 4,5 } - \frac{\sqrt[5]{9} }{\sqrt[5]{288} }[/tex]. Created by Miа16. algebra-ru

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mmb1

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$\sqrt[5]{1 \frac{11}{16}*4,5 } - \frac{\sqrt[5]{9} }{\sqrt[5]{288} } = 1$

⁵√9/⁵√288 = ⁵√(1/32) = ⁵√1/2⁵ = 1/2

⁵√(1 11/16 * 4.5) = ⁵√(27/16 * 9/2) = ⁵√(3/2)⁵ = 3/2

3/2 - 1/2 = 1

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sangers1959

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Объяснение:

$\sqrt[5]{1\frac{11}{16}*4,5 }-\frac{\sqrt[5]{9} }{\sqrt[5]{288} } =\sqrt[5]{\frac{27}{16}*4\frac{1}{2} } -\sqrt[5]{\frac{9}{288} } =\sqrt[5]{\frac{27}{16}*\frac{9}{2} }-\sqrt[5]{\frac{1}{32} }=\\=\sqrt[5]{\frac{243}{32} } -\sqrt[5]{\frac{1}{32} } =\sqrt[5]{\frac{3^5}{2^5}}+\sqrt[5]{\frac{1^5}{2^5} } }=\sqrt[5]{(\frac{3}{2})^5 }-\sqrt[5]{(\frac{1}{2})^5 }= \frac{3}{2}-\frac{1}{2}=1.$

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