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Simplify the square root of 16y^4. Assume that the variable y represents a positive...

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javaria95 | Student, Grade 10 | (Level 1) Honors

Posted January 26, 2012 at 11:33 AM via web

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Simplify the square root of 16y^4. Assume that the variable y represents a positive real number?

 

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted January 26, 2012 at 11:55 AM (Answer #1)

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Think 4*4*y*y*y*y.  Now we need to factor this into two equal groups:

4*y*y * 4*y*y

`4y^2*4y^2`

So `sqrt(16y^4)` = `4y^2`

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted January 26, 2012 at 1:39 PM (Answer #2)

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Though the only answer posted by nathanshields is rated "The Best" by the question asker, it may be argued to be 'not true' as under:

given y is a positive real number, the number 16y^4 can be seen to be made up as:

          4*y^2 * 4*y^2

and

          (-4)*y^2 * (-4)*y^2

Hence there would be 2 square roots of 16y^4 as 4y^2 and -4y^2

It is to be noted that the question asker did not mention that the sqare-roots have to be positive real numbers but "y" is a positive real number which is true for both the square roots. 

 

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