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Simplify: Type the Answer as a Radical Reduced to the Simplest form

Radical 567x^{2}y^{4}z^{2} with a 4 index

ManuelBautista2019
Feb 13, 2018

#5**+2 **

ManuelBautista2019, I am certain that the preceding answerers have misinterpreted the question.

You mean \(\sqrt[4]{567x^2y^4z^2}\). Notice that this expression has a radical with an index of 4!

\(\sqrt[4]{567x^2y^4z^2}\\ \sqrt[4]{3^4*7*x^2*y^4*z^2}\\ 3|y|\sqrt[4]{7x^2z^2}\)

This radical is now in simplest form. And, yes, the absolute value bars around y is deliberate and intentional.

y^4 will always be positive--whether or not y is positive or negative. Taking the 4th root of a number implies the **principal root**, or the positive answer, so y cannot be negative. We account for this by adding absolute value bars.

TheXSquaredFactor
Feb 14, 2018

#5**+2 **

Best Answer

ManuelBautista2019, I am certain that the preceding answerers have misinterpreted the question.

You mean \(\sqrt[4]{567x^2y^4z^2}\). Notice that this expression has a radical with an index of 4!

\(\sqrt[4]{567x^2y^4z^2}\\ \sqrt[4]{3^4*7*x^2*y^4*z^2}\\ 3|y|\sqrt[4]{7x^2z^2}\)

This radical is now in simplest form. And, yes, the absolute value bars around y is deliberate and intentional.

y^4 will always be positive--whether or not y is positive or negative. Taking the 4th root of a number implies the **principal root**, or the positive answer, so y cannot be negative. We account for this by adding absolute value bars.

TheXSquaredFactor
Feb 14, 2018