Square Root Calculator › Square root of 510
Square Root of 510
√510 ≈ 22.58318
510 is not a perfect square, so √510 is an irrational number that is approximately 22.58318. In simplified radical form, √510 = √510.
√510 lies between √484 = 22 and √529 = 23.
| Number | 510 |
| Square root (decimal) | 22.58318 |
| Simplified radical | √510 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 510
510 = 2 × 3 × 5 × 17. This is what determines the simplified radical: for √510 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √510 is already in simplest radical form as √510.
Estimating √510 by hand
√510 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 510 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.590909 |
| Step 2 | 22.583181 |
| Step 3 | 22.58318 |
After 3 steps the estimate is 22.58318, matching √510 ≈ 22.58318.
Nearby square roots
Frequently asked questions
Is 510 a perfect square?
No, 510 is not a perfect square, so its square root is irrational and approximately 22.58318.
What is the square root of 510 in simplest radical form?
√510 = √510 in simplest radical form.