Hex Square Root Calculator
Find the square root of a hex value — exact for perfect squares, with the leftover remainder shown for everything else instead of a rounded decimal.
How Hex Square Root Works
The calculator finds the largest whole number whose square doesn't exceed the input value. For a perfect square, that's the exact answer. Otherwise, it's the floor of the true square root, shown alongside the remainder — how far the root squared falls short of the original value.
Hex Square Root Example, Step by Step
sqrt(1A3) = 14 remainder 19
sqrt(0x1A3) = 0x14, remainder 19
1A3 hex = 419 decimal 20^2 = 400 (<= 419) 21^2 = 441 (> 419) Root = 20, remainder = 419 - 400 = 19 20 decimal = 14 hex
| Step | Description | Result |
|---|---|---|
| Convert 1A3 | 1A3 (hex) = 419 (decimal) | 419 |
| Find the largest root | 20^2 = 400 fits; 21^2 = 441 doesn't | 20 |
| Find the remainder | 419 - 400 = 19 | 19 |
| Convert root to hex | 20 (decimal) = 14 (hex) | 14 |
Try 100 in the calculator above for a perfect-square example — it resolves cleanly to 10 hex with no remainder.
Common Mistakes With Hex Square Root
- Expecting an exact decimal answer for non-perfect squares instead of a floored root plus remainder.
- Assuming every hex value has a whole-number square root.
- Trying to take the square root of a negative value, which isn't supported here.
Frequently Asked Questions
How do you find the square root of a hex value?
Convert to decimal and find the largest whole number whose square doesn't exceed it. This calculator uses an integer square root algorithm (Newton's method) rather than floating-point math, so results stay exact.
What does it mean when the result shows a remainder?
It means the value isn't a perfect square — the shown root is the floor of the true square root, and the remainder is how much is left over (value minus root squared), the same idea as a division remainder.
What's a perfect square in hex?
A value that's the exact square of another whole number — 0x100 (256) is a perfect square because it's exactly 16^2, so its square root shows with no remainder.
Why use an integer algorithm instead of just computing sqrt() with floating point?
Floating-point math loses precision on very large numbers. This calculator's arbitrary-precision integer approach stays exact no matter how large the input hex value is.
Can I take the square root of a negative hex value?
No — hex values here are treated as non-negative magnitudes, and square roots of negative numbers aren't real numbers, so this calculator doesn't support that case.
Is this the reverse of the Hex Square Calculator?
Yes — squaring and square root undo each other for perfect squares. For non-perfect squares, squaring the floored root gets you close to, but not exactly, the original value.