Question

How do you simplify `sqrt(196y^10)`?

Answer 1

`sqrt(196y^10) = 14y^5`

Explanation:

`14xx14 = 196`
`y^5xxy^5=y^10`

So `sqrt(196y^10) = sqrt(14^2(y^5)^2)`

`color(white)("XXXXXX")= abs(14y^5)`
...we take the absolute value to ensure the root extracted is the principal root

Answer 2

`sqrt(196y^10) = 14abs(y^5)`

Explanation:

First, note that in general `sqrt(x^2) = abs(x)` rather than `x`,

since:

`sqrt(x^2) = { (x, "if x >= 0"), (-x, "if x < 0") :}`

Also, if `a, b >= 0` then `sqrt(ab) = sqrt(a)sqrt(b)`

So:

`sqrt(196y^10) = sqrt(14^2 (y^5)^2) = sqrt(14^2)sqrt((y^5)^2) = 14abs(y^5)`