Notice that the expression under the square root is a perfect square:

$x^4 + 6x^2 + 9 = (x^2)^2 + 2(x^2)(3) + 3^2 = (x^2 + 3)^2$

Therefore: $\sqrt{x^4 + 6x^2 + 9} = \sqrt{(x^2 + 3)^2} = |x^2 + 3|$

Since $x^2 \geq 0$ for all real $x$, we have $x^2 + 3 \geq 3 > 0$, which means $x^2 + 3$ is always positive.

Thus: $|x^2 + 3| = x^2 + 3$

Therefore, Column A equals Column B, so the answer is C (the two quantities are equal).