Square Root Calculator › Square root of 454
Square Root of 454
√454 ≈ 21.307276
454 is not a perfect square, so √454 is an irrational number that is approximately 21.307276. In simplified radical form, √454 = √454.
√454 lies between √441 = 21 and √484 = 22.
| Number | 454 |
| Square root (decimal) | 21.307276 |
| Simplified radical | √454 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 454
454 = 2 × 227. This is what determines the simplified radical: for √454 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √454 is already in simplest radical form as √454.
Estimating √454 by hand
√454 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 454 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.309524 |
| Step 2 | 21.307276 |
| Step 3 | 21.307276 |
After 3 steps the estimate is 21.307276, matching √454 ≈ 21.307276.
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Frequently asked questions
Is 454 a perfect square?
No, 454 is not a perfect square, so its square root is irrational and approximately 21.307276.
What is the square root of 454 in simplest radical form?
√454 = √454 in simplest radical form.