sqrt()

/* <number> 値 */
width: calc(100px * sqrt(9)); /*  300px */
width: calc(100px * sqrt(25)); /*  500px */
width: calc(100px * sqrt(100)); /* 1000px */

<div class="boxes">
  <div class="box">50px</div>
  <div class="box one">100px</div>
  <div class="box two">150px</div>
  <div class="box three">200px</div>
</div>

:root {
  --size-0: 50px;
  --size-1: calc(var(--size-0) * sqrt(4)); /*  100px */
  --size-2: calc(var(--size-0) * sqrt(9)); /*  150px */
  --size-3: calc(var(--size-0) * sqrt(16)); /*  200px */
}

.boxes {
  display: flex;
  flex-wrap: wrap;
  justify-content: space-around;
}
.box {
  width: var(--size-0);
  height: var(--size-0);
  background-color: tomato;
  color: white;
  display: flex;
  align-items: center;
  justify-content: center;
}

.one {
  width: var(--size-1);
  height: var(--size-1);
}
.two {
  width: var(--size-2);
  height: var(--size-2);
}
.three {
  width: var(--size-3);
  height: var(--size-3);
}