Question

Simplify the radical expression.

4 sqrt 625x^12y^8

Answer 1

`\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}`