Square Root Calculator › Square root of 516
Square Root of 516
√516 ≈ 22.715633
516 is not a perfect square, so √516 is an irrational number that is approximately 22.715633. In simplified radical form, √516 = 2√129.
√516 lies between √484 = 22 and √529 = 23.
| Number | 516 |
| Square root (decimal) | 22.715633 |
| Simplified radical | 2√129 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 516
516 = 2^2 × 3 × 43. This is what determines the simplified radical: for √516 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √516 = 2√129.
Estimating √516 by hand
√516 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 516 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.727273 |
| Step 2 | 22.715636 |
| Step 3 | 22.715633 |
After 3 steps the estimate is 22.715633, matching √516 ≈ 22.715633.
Nearby square roots
Frequently asked questions
Is 516 a perfect square?
No, 516 is not a perfect square, so its square root is irrational and approximately 22.715633.
What is the square root of 516 in simplest radical form?
√516 = 2√129 in simplest radical form.