How do you multiply radical expressions?

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How do you multiply radical expressions?

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Answer 1 · 2015-03-22T22:04:06

One method is to make one big radical, then simplify.

$\sqrt[3]{2 x^{2} y^{6}} \sqrt[3]{20 x y^{4}} = \sqrt[3]{2 x^{2} y^{6} \cdot 20 x^{2} y^{4}}$ $root(3)(2x^2y^6)root(3)(20xy^4)=root(3)(2x^2y^6*20x^2y^4)$

$= \sqrt[3]{40 x^{3} y^{10}} = \sqrt[3]{8 \cdot 5 x^{3} y^{9} y} = 2 x y^{3} \sqrt[3]{5 y}$ $=root(3)(40x^3y^10)=root(3)(8*5x^3y^9y)=2xy^3root(3)(5y)$

Or simplify first, then combine what's left and simplify again:

$\sqrt[3]{2 x^{2} y^{6}} \sqrt[3]{20 x y^{4}} = [y^{2} \sqrt[3]{2 x^{2}}] [y \sqrt[3]{20 x y}]$ $root(3)(2x^2y^6)root(3)(20xy^4)=[y^2root(3)(2x^2)][yroot(3)(20xy)]$

$= y^{3} \sqrt[3]{40 x^{3} y} = 2 x y^{3} \sqrt[3]{5 y}$ $=y^3root(3)(40x^3y)=2xy^3root(3)(5y)$ .

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How do you multiply radical expressions?

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