Square Root Calculator › Square root of 437
Square Root of 437
√437 ≈ 20.904545
437 is not a perfect square, so √437 is an irrational number that is approximately 20.904545. In simplified radical form, √437 = √437.
√437 lies between √400 = 20 and √441 = 21.
| Number | 437 |
| Square root (decimal) | 20.904545 |
| Simplified radical | √437 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 437
437 = 19 × 23. This is what determines the simplified radical: for √437 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √437 is already in simplest radical form as √437.
Estimating √437 by hand
√437 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 437 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.925 |
| Step 2 | 20.904555 |
| Step 3 | 20.904545 |
After 3 steps the estimate is 20.904545, matching √437 ≈ 20.904545.
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Frequently asked questions
Is 437 a perfect square?
No, 437 is not a perfect square, so its square root is irrational and approximately 20.904545.
What is the square root of 437 in simplest radical form?
√437 = √437 in simplest radical form.