How to simplify $\sqrt[3]{24 y^{21} x^{5}}$ $root(3)(24y^21x^5)$ ?

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How to simplify $\sqrt[3]{24 y^{21} x^{5}}$ $root(3)(24y^21x^5)$ ?

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Answer 1 · 2017-04-02T18:39:43

$2 x y^{7} \sqrt[3]{2 x^{2}}$ $2xy^7root(3)(2x^2)$

Explanation:

Write the radicand as aproduct of prime factors.

$\sqrt[3]{24 y^{21} x^{5}} = \sqrt[3]{3 \times 2^{3} y^{21} x^{5}}$ $root(3) (24y^21x^5) =root(3) (3xx2^3y^21x^5)$

Write cubes where possible:
$\sqrt[3]{3 \times 2^{3} y^{21} x^{5}} = \sqrt[3]{3 \times 2^{3} y^{21} x^{3} \times x^{2}}$ $root(3) (3xx2^3y^21x^5) = root(3) (3xxcolor(red)(2^3y^21x^3)xx x^2)$

Find the cube roots where possible by dividing the indices by $3$ $3$ .

$= 2 x y^{7} \sqrt[3]{2 x^{2}}$ $=color(red)(2xy^7)root(3)(2x^2)$

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How to simplify $\sqrt[3]{24 y^{21} x^{5}}$ $root(3)(24y^21x^5)$ ?

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Science

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Humanities

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How to simplify 3√24y21x5root(3)(24y^21x^5) ?

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Explanation:

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How to simplify $\sqrt[3]{24 y^{21} x^{5}}$ $root(3)(24y^21x^5)$ ?