Square Root Calculator › Square root of 372
Square Root of 372
√372 ≈ 19.287302
372 is not a perfect square, so √372 is an irrational number that is approximately 19.287302. In simplified radical form, √372 = 2√93.
√372 lies between √361 = 19 and √400 = 20.
| Number | 372 |
| Square root (decimal) | 19.287302 |
| Simplified radical | 2√93 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 372
372 = 2^2 × 3 × 31. This is what determines the simplified radical: for √372 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √372 = 2√93.
Estimating √372 by hand
√372 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 372 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.289474 |
| Step 2 | 19.287302 |
| Step 3 | 19.287302 |
After 3 steps the estimate is 19.287302, matching √372 ≈ 19.287302.
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Frequently asked questions
Is 372 a perfect square?
No, 372 is not a perfect square, so its square root is irrational and approximately 19.287302.
What is the square root of 372 in simplest radical form?
√372 = 2√93 in simplest radical form.