Square Root Calculator › Square root of 432
Square Root of 432
√432 ≈ 20.78461
432 is not a perfect square, so √432 is an irrational number that is approximately 20.78461. In simplified radical form, √432 = 12√3.
√432 lies between √400 = 20 and √441 = 21.
| Number | 432 |
| Square root (decimal) | 20.78461 |
| Simplified radical | 12√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 432
432 = 2^4 × 3^3. This is what determines the simplified radical: for √432 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √432 = 12√3.
Estimating √432 by hand
√432 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 432 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.8 |
| Step 2 | 20.784615 |
| Step 3 | 20.78461 |
After 3 steps the estimate is 20.78461, matching √432 ≈ 20.78461.
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Frequently asked questions
Is 432 a perfect square?
No, 432 is not a perfect square, so its square root is irrational and approximately 20.78461.
What is the square root of 432 in simplest radical form?
√432 = 12√3 in simplest radical form.