The latency for sqrtss on broadwell is 11 cycles with a throughput of 4, where mul is a latency of 3 and throughput of 1. So, using some concrete numbers, sqrt is more expensive, but not polynomially or even an order of magnitude.
Conversions are still somewhat expensive, but I do know compared to polynomial time or a large enough constant, it can be a better choice for an optimization. For example, computing log10 of an integer.