Square Root Calculator › Square root of 440
Square Root of 440
√440 ≈ 20.976177
440 is not a perfect square, so √440 is an irrational number that is approximately 20.976177. In simplified radical form, √440 = 2√110.
√440 lies between √400 = 20 and √441 = 21.
| Number | 440 |
| Square root (decimal) | 20.976177 |
| Simplified radical | 2√110 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 440
440 = 2^3 × 5 × 11. This is what determines the simplified radical: for √440 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √440 = 2√110.
Estimating √440 by hand
√440 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 440 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 21 |
| Step 2 | 20.97619 |
| Step 3 | 20.976177 |
After 3 steps the estimate is 20.976177, matching √440 ≈ 20.976177.
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Frequently asked questions
Is 440 a perfect square?
No, 440 is not a perfect square, so its square root is irrational and approximately 20.976177.
What is the square root of 440 in simplest radical form?
√440 = 2√110 in simplest radical form.