Square Root Calculator › Square root of 434
Square Root of 434
√434 ≈ 20.832667
434 is not a perfect square, so √434 is an irrational number that is approximately 20.832667. In simplified radical form, √434 = √434.
√434 lies between √400 = 20 and √441 = 21.
| Number | 434 |
| Square root (decimal) | 20.832667 |
| Simplified radical | √434 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 434
434 = 2 × 7 × 31. This is what determines the simplified radical: for √434 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √434 is already in simplest radical form as √434.
Estimating √434 by hand
√434 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 434 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.85 |
| Step 2 | 20.832674 |
| Step 3 | 20.832667 |
After 3 steps the estimate is 20.832667, matching √434 ≈ 20.832667.
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Frequently asked questions
Is 434 a perfect square?
No, 434 is not a perfect square, so its square root is irrational and approximately 20.832667.
What is the square root of 434 in simplest radical form?
√434 = √434 in simplest radical form.