Square Root Calculator › Square root of 460
Square Root of 460
√460 ≈ 21.447611
460 is not a perfect square, so √460 is an irrational number that is approximately 21.447611. In simplified radical form, √460 = 2√115.
√460 lies between √441 = 21 and √484 = 22.
| Number | 460 |
| Square root (decimal) | 21.447611 |
| Simplified radical | 2√115 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 460
460 = 2^2 × 5 × 23. This is what determines the simplified radical: for √460 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √460 = 2√115.
Estimating √460 by hand
√460 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 460 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.452381 |
| Step 2 | 21.447611 |
| Step 3 | 21.447611 |
After 3 steps the estimate is 21.447611, matching √460 ≈ 21.447611.
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Frequently asked questions
Is 460 a perfect square?
No, 460 is not a perfect square, so its square root is irrational and approximately 21.447611.
What is the square root of 460 in simplest radical form?
√460 = 2√115 in simplest radical form.