Square Root Calculator › Square root of 515
Square Root of 515
√515 ≈ 22.693611
515 is not a perfect square, so √515 is an irrational number that is approximately 22.693611. In simplified radical form, √515 = √515.
√515 lies between √484 = 22 and √529 = 23.
| Number | 515 |
| Square root (decimal) | 22.693611 |
| Simplified radical | √515 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 515
515 = 5 × 103. This is what determines the simplified radical: for √515 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √515 is already in simplest radical form as √515.
Estimating √515 by hand
√515 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 515 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.704545 |
| Step 2 | 22.693614 |
| Step 3 | 22.693611 |
After 3 steps the estimate is 22.693611, matching √515 ≈ 22.693611.
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Frequently asked questions
Is 515 a perfect square?
No, 515 is not a perfect square, so its square root is irrational and approximately 22.693611.
What is the square root of 515 in simplest radical form?
√515 = √515 in simplest radical form.