Square Root Calculator › Square root of 264
Square Root of 264
√264 ≈ 16.248077
264 is not a perfect square, so √264 is an irrational number that is approximately 16.248077. In simplified radical form, √264 = 2√66.
√264 lies between √256 = 16 and √289 = 17.
| Number | 264 |
| Square root (decimal) | 16.248077 |
| Simplified radical | 2√66 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 264
264 = 2^3 × 3 × 11. This is what determines the simplified radical: for √264 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √264 = 2√66.
Estimating √264 by hand
√264 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 264 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.25 |
| Step 2 | 16.248077 |
| Step 3 | 16.248077 |
After 3 steps the estimate is 16.248077, matching √264 ≈ 16.248077.
Nearby square roots
Frequently asked questions
Is 264 a perfect square?
No, 264 is not a perfect square, so its square root is irrational and approximately 16.248077.
What is the square root of 264 in simplest radical form?
√264 = 2√66 in simplest radical form.