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Simplify the radical expression.

4 sqrt 625x^12y^8

User Oriadam
by
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1 Answer

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Answer:


\sqrt[4]{625x^(12)y^8} = 5 {x^3} {y^2}

Explanation:

Given


\sqrt[4]{625x^(12)y^8}

Required

Simplify

We start by splitting the roots


\sqrt[4]{625x^(12)y^8} = \sqrt[4]{625}* \sqrt[4]{x^(12)} * \sqrt[4]{y^8}

Express 625 as exponents


\sqrt[4]{625x^(12)y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^(12)} * \sqrt[4]{y^8}

From laws of indices


\sqrt[n]{a^m} = a^{(m)/(n)}

So,


\sqrt[4]{625x^(12)y^8} = \sqrt[4]{5^4}* \sqrt[4]{x^(12)} * \sqrt[4]{y^8} becomes


\sqrt[4]{625x^(12)y^8} = {5^(4)/(4)} * {x^(12)/(4)} * {y^(8)/(4)}


\sqrt[4]{625x^(12)y^8} = 5 * {x^3} * {y^2}


\sqrt[4]{625x^(12)y^8} = 5 {x^3} {y^2}

User Erick Martinez
by
6.8k points