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Stephen
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Tyro
Asked: 2021-04-06T06:27:58+00:00 In: ,

Simplifying radicals expressions using the law of radicals

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√32x^3y^5

simplifying

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1 Answer

  2. acedstud

    I am not sure which of the factors is covered by the radical sign. However, I will solve the question assuming the radical sign covers all the factors.

    \sqrt{32x^3y^5}=\left(32x^3y^5\right)^{\frac{1}{2}}=32^{\frac{1}{2}}x^{\frac{3}{2}}y^{\frac{5}{2}}

    =(16\times2)^{\frac{1}{2}}x^{1+\frac{1}{2}}y^{2+\frac{1}{2}}=4\cdot2^{\frac{1}{2}}\cdot x\cdot x^{\frac{1}{2}}\cdot y^2\cdot y^{\frac{1}{2}}

    =4xy^2(2xy)^{\frac{1}{2}}=4xy^2\sqrt{2xy}

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