Square Root Calculator › Square root of 204
Square Root of 204
√204 ≈ 14.282857
204 is not a perfect square, so √204 is an irrational number that is approximately 14.282857. In simplified radical form, √204 = 2√51.
√204 lies between √196 = 14 and √225 = 15.
| Number | 204 |
| Square root (decimal) | 14.282857 |
| Simplified radical | 2√51 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 204
204 = 2^2 × 3 × 17. This is what determines the simplified radical: for √204 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √204 = 2√51.
Estimating √204 by hand
√204 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 204 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.285714 |
| Step 2 | 14.282857 |
| Step 3 | 14.282857 |
After 3 steps the estimate is 14.282857, matching √204 ≈ 14.282857.
Nearby square roots
Frequently asked questions
Is 204 a perfect square?
No, 204 is not a perfect square, so its square root is irrational and approximately 14.282857.
What is the square root of 204 in simplest radical form?
√204 = 2√51 in simplest radical form.