Square Root Calculator › Square root of 453
Square Root of 453
√453 ≈ 21.283797
453 is not a perfect square, so √453 is an irrational number that is approximately 21.283797. In simplified radical form, √453 = √453.
√453 lies between √441 = 21 and √484 = 22.
| Number | 453 |
| Square root (decimal) | 21.283797 |
| Simplified radical | √453 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 453
453 = 3 × 151. This is what determines the simplified radical: for √453 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √453 is already in simplest radical form as √453.
Estimating √453 by hand
√453 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 453 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.285714 |
| Step 2 | 21.283797 |
| Step 3 | 21.283797 |
After 3 steps the estimate is 21.283797, matching √453 ≈ 21.283797.
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Frequently asked questions
Is 453 a perfect square?
No, 453 is not a perfect square, so its square root is irrational and approximately 21.283797.
What is the square root of 453 in simplest radical form?
√453 = √453 in simplest radical form.