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

*print*Print*list*Cite

### 2 Answers

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`

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.