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

Asked on by javaria95

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Top Answer

nathanshields's profile pic

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

Posted on

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

4*y*y * 4*y*y


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

najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

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


          (-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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