# Thread: square root of an even power

1. ## square root of an even power

sqrt(4x^2 + 9x^4) = sqrt(x^2*(4+9x^2)) = |x|*sqrt(4+9x^2)) is that absolute value sign always necessary when you take out an x squared from under the radical? what if it is something like

sqrt(4*t^2*sin^2(t^2)+4*t^2*cos^2(t^2)))
does that turn out to be |2t|*sqrt(sin^2(t^2)+cos^2(t^2))

2. Originally Posted by zintore
sqrt(4x^2 + 9x^4) = sqrt(x^2*(4+9x^2)) = |x|*sqrt(4+9x^2)) is that absolute value sign always necessary when you take out an x squared from under the radical? what if it is something like

sqrt(4*t^2*sin^2(t^2)+4*t^2*cos^2(t^2)))
does that turn out to be |2t|*sqrt(sin^2(t^2)+cos^2(t^2))
Yes you need to take absolute value. Because otherwise it would mean sqrt[ (-1)^2 ] = -1 which is wrong.