Today's soundtrack is Agalloch: Of Stone, Wind, & Pillor, a gorgeous blackened folk metal album - technically an EP, but it's nearly 30 minutes long, and it stands alone just fine!
When comparing a linear graph of a function vs the square root of that function, invariant points will always occur at y 0 and y 1. Between those values, there is a slight bow in the radical function's graph which is caused by the fact that values between 0 and 1 are larger in radical form (for example, the square root of 0.5 is 0.7).