Square Root Calculator › Square root of 433
Square Root of 433
√433 ≈ 20.808652
433 is not a perfect square, so √433 is an irrational number that is approximately 20.808652. In simplified radical form, √433 = √433.
√433 lies between √400 = 20 and √441 = 21.
| Number | 433 |
| Square root (decimal) | 20.808652 |
| Simplified radical | √433 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 433
433 = 433. This is what determines the simplified radical: for √433 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √433 is already in simplest radical form as √433.
Estimating √433 by hand
√433 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 433 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.825 |
| Step 2 | 20.808658 |
| Step 3 | 20.808652 |
After 3 steps the estimate is 20.808652, matching √433 ≈ 20.808652.
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Frequently asked questions
Is 433 a perfect square?
No, 433 is not a perfect square, so its square root is irrational and approximately 20.808652.
What is the square root of 433 in simplest radical form?
√433 = √433 in simplest radical form.