Question

How do you simplify `sqrt(8x^2)`?

Answer 1

`sqrt(8x^2) = 2sqrt(2)abs(x)`

Explanation:

`sqrt(8x^2)`
`color(white)("XXX")=sqrt(2^2*2*x^2)`
`color(white)("XXX")=sqrt(2^2)*sqrt(2)*sqrt(x^2)`
`color(white)("XXX")=2sqrt(2)abs(x)`

Note, by convention, `sqrt(q)` for `q in RR^(0+)` is the primary (non-negative) square root and therefore it is necessary to take the absolute value of `x` when evaluating `sqrt(x^2)`