Square Root Calculator › Square root of 436
Square Root of 436
√436 ≈ 20.880613
436 is not a perfect square, so √436 is an irrational number that is approximately 20.880613. In simplified radical form, √436 = 2√109.
√436 lies between √400 = 20 and √441 = 21.
| Number | 436 |
| Square root (decimal) | 20.880613 |
| Simplified radical | 2√109 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 436
436 = 2^2 × 109. This is what determines the simplified radical: for √436 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √436 = 2√109.
Estimating √436 by hand
√436 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 436 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.9 |
| Step 2 | 20.880622 |
| Step 3 | 20.880613 |
After 3 steps the estimate is 20.880613, matching √436 ≈ 20.880613.
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Frequently asked questions
Is 436 a perfect square?
No, 436 is not a perfect square, so its square root is irrational and approximately 20.880613.
What is the square root of 436 in simplest radical form?
√436 = 2√109 in simplest radical form.