sqrt()

double sqrt(double x);

void setup() {
    pinLabel(0, "IN");   // set the label of pin 0 to "IN"
    pinLabel(1, "OUT");  // set the label of pin 1 to "OUT"
    pinMode(1, OUTPUT);  // set pin 1 as output

    pinLabel(2, "VCC");  // set the label of pin 2 to "VCC"
    powerPin(2);         // set pin 2 as power pin
    pinLabel(3, "GND");  // set the label of pin 3 to "GND"
    groundPin(3);        // set pin 3 as ground pin
}

void loop() {
    // read the value of the potentiometer
    int val = analogRead(0);
    // map the value of the potentiometer from 0 to 1023
    // to the range of 0 to 5
    double x = map(val, 0, 1023, 0, 5);
    // calculate the square root of x
    double y = sqrt(x);
    // map the value of y from 0 to 2.23607 to 0 to 1023
    int pwm = (int) map(y, 0, 2.23607, 0, 1023);
    // write the value of pwm to pin 1
    analogWrite(1, pwm);
}