Square Root Calculator › Square root of 431
Square Root of 431
√431 ≈ 20.760539
431 is not a perfect square, so √431 is an irrational number that is approximately 20.760539. In simplified radical form, √431 = √431.
√431 lies between √400 = 20 and √441 = 21.
| Number | 431 |
| Square root (decimal) | 20.760539 |
| Simplified radical | √431 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 431
431 = 431. This is what determines the simplified radical: for √431 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √431 is already in simplest radical form as √431.
Estimating √431 by hand
√431 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 431 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.775 |
| Step 2 | 20.760545 |
| Step 3 | 20.760539 |
After 3 steps the estimate is 20.760539, matching √431 ≈ 20.760539.
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Frequently asked questions
Is 431 a perfect square?
No, 431 is not a perfect square, so its square root is irrational and approximately 20.760539.
What is the square root of 431 in simplest radical form?
√431 = √431 in simplest radical form.