Square Root Calculator › Square root of 520
Square Root of 520
√520 ≈ 22.803509
520 is not a perfect square, so √520 is an irrational number that is approximately 22.803509. In simplified radical form, √520 = 2√130.
√520 lies between √484 = 22 and √529 = 23.
| Number | 520 |
| Square root (decimal) | 22.803509 |
| Simplified radical | 2√130 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 520
520 = 2^3 × 5 × 13. This is what determines the simplified radical: for √520 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √520 = 2√130.
Estimating √520 by hand
√520 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 520 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.818182 |
| Step 2 | 22.803513 |
| Step 3 | 22.803509 |
After 3 steps the estimate is 22.803509, matching √520 ≈ 22.803509.
Nearby square roots
Frequently asked questions
Is 520 a perfect square?
No, 520 is not a perfect square, so its square root is irrational and approximately 22.803509.
What is the square root of 520 in simplest radical form?
√520 = 2√130 in simplest radical form.