+0  
 
+1
338
5
avatar+1451 

Help me please

 

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

 

Radical 567x2y4z2 with a 4 index

 Feb 13, 2018

Best Answer 

 #5
avatar+2346 
+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.

 Feb 14, 2018
edited by TheXSquaredFactor  Feb 14, 2018
 #1
avatar+429 
+1

Ans:567^4x^8y^16z^8

 

smileysmileysmiley

 Feb 13, 2018
 #2
avatar+557 
+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

 

 

winkwinkwink        

 Feb 13, 2018
edited by lynx7  Feb 13, 2018
edited by lynx7  Feb 13, 2018
 #3
avatar+1451 
+1

what about the index?

 Feb 13, 2018
 #4
avatar+429 
+1

I included the index.

 

smileysmileysmiley

qualitystreet  Feb 13, 2018
 #5
avatar+2346 
+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
edited by TheXSquaredFactor  Feb 14, 2018

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