Square Root Calculator › Square root of 435
Square Root of 435
√435 ≈ 20.856654
435 is not a perfect square, so √435 is an irrational number that is approximately 20.856654. In simplified radical form, √435 = √435.
√435 lies between √400 = 20 and √441 = 21.
| Number | 435 |
| Square root (decimal) | 20.856654 |
| Simplified radical | √435 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 435
435 = 3 × 5 × 29. This is what determines the simplified radical: for √435 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √435 is already in simplest radical form as √435.
Estimating √435 by hand
√435 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 435 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.875 |
| Step 2 | 20.856662 |
| Step 3 | 20.856654 |
After 3 steps the estimate is 20.856654, matching √435 ≈ 20.856654.
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Frequently asked questions
Is 435 a perfect square?
No, 435 is not a perfect square, so its square root is irrational and approximately 20.856654.
What is the square root of 435 in simplest radical form?
√435 = √435 in simplest radical form.