Square Root Calculator › Square root of 556
Square Root of 556
√556 ≈ 23.579652
556 is not a perfect square, so √556 is an irrational number that is approximately 23.579652. In simplified radical form, √556 = 2√139.
√556 lies between √529 = 23 and √576 = 24.
| Number | 556 |
| Square root (decimal) | 23.579652 |
| Simplified radical | 2√139 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 556
556 = 2^2 × 139. This is what determines the simplified radical: for √556 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √556 = 2√139.
Estimating √556 by hand
√556 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 556 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.586957 |
| Step 2 | 23.579653 |
| Step 3 | 23.579652 |
After 3 steps the estimate is 23.579652, matching √556 ≈ 23.579652.
Nearby square roots
Frequently asked questions
Is 556 a perfect square?
No, 556 is not a perfect square, so its square root is irrational and approximately 23.579652.
What is the square root of 556 in simplest radical form?
√556 = 2√139 in simplest radical form.