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

Radical 567x2y4z2 with a 4 index

Feb 13, 2018

#5
+2

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

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

$$\sqrt{567x^2y^4z^2}\\ \sqrt{3^4*7*x^2*y^4*z^2}\\ 3|y|\sqrt{7x^2z^2}$$

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.

Feb 14, 2018
edited by TheXSquaredFactor  Feb 14, 2018

#1
+1

Ans:567^4x^8y^16z^8   Feb 13, 2018
#2
+1

√ [ 567 * x^2 * y^4 * z^2]

√567 * √x^2 * √y^4 * √z^2

9 * √7 * √x^2 * √y^4 * √z^2

9 * √7 * x * y^2 * z

9xy^2z√7

(9xy^2z√7)^2

=81x^2y^4z^2*7   Feb 13, 2018
edited by lynx7  Feb 13, 2018
edited by lynx7  Feb 13, 2018
#3
+1

Feb 13, 2018
#4
+1

I included the index.   qualitystreet  Feb 13, 2018
#5
+2

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

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

$$\sqrt{567x^2y^4z^2}\\ \sqrt{3^4*7*x^2*y^4*z^2}\\ 3|y|\sqrt{7x^2z^2}$$

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
edited by TheXSquaredFactor  Feb 14, 2018