Square Root Calculator › Square root of 455
Square Root of 455
√455 ≈ 21.330729
455 is not a perfect square, so √455 is an irrational number that is approximately 21.330729. In simplified radical form, √455 = √455.
√455 lies between √441 = 21 and √484 = 22.
| Number | 455 |
| Square root (decimal) | 21.330729 |
| Simplified radical | √455 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 455
455 = 5 × 7 × 13. This is what determines the simplified radical: for √455 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √455 is already in simplest radical form as √455.
Estimating √455 by hand
√455 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 455 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.333333 |
| Step 2 | 21.330729 |
| Step 3 | 21.330729 |
After 3 steps the estimate is 21.330729, matching √455 ≈ 21.330729.
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Frequently asked questions
Is 455 a perfect square?
No, 455 is not a perfect square, so its square root is irrational and approximately 21.330729.
What is the square root of 455 in simplest radical form?
√455 = √455 in simplest radical form.