Square Root Calculator › Square root of 430
Square Root of 430
√430 ≈ 20.736441
430 is not a perfect square, so √430 is an irrational number that is approximately 20.736441. In simplified radical form, √430 = √430.
√430 lies between √400 = 20 and √441 = 21.
| Number | 430 |
| Square root (decimal) | 20.736441 |
| Simplified radical | √430 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 430
430 = 2 × 5 × 43. This is what determines the simplified radical: for √430 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √430 is already in simplest radical form as √430.
Estimating √430 by hand
√430 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 430 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.75 |
| Step 2 | 20.736446 |
| Step 3 | 20.736441 |
After 3 steps the estimate is 20.736441, matching √430 ≈ 20.736441.
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Frequently asked questions
Is 430 a perfect square?
No, 430 is not a perfect square, so its square root is irrational and approximately 20.736441.
What is the square root of 430 in simplest radical form?
√430 = √430 in simplest radical form.