Maintain x*x in C++

I have the following while-loop

uint32_t x = 0;
while(x*x < STOP_CONDITION) {
    if(CHECK_CONDITION) x++
    // Do other stuff that modifies CHECK_CONDITION
}

The STOP_CONDITION is constant at run-time, but not at compile time. Is there are more efficient way to maintain x*x or do I really need to recompute it every time?