Square Root Calculator › Square root of 374
Square Root of 374
√374 ≈ 19.33908
374 is not a perfect square, so √374 is an irrational number that is approximately 19.33908. In simplified radical form, √374 = √374.
√374 lies between √361 = 19 and √400 = 20.
| Number | 374 |
| Square root (decimal) | 19.33908 |
| Simplified radical | √374 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 374
374 = 2 × 11 × 17. This is what determines the simplified radical: for √374 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √374 is already in simplest radical form as √374.
Estimating √374 by hand
√374 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 374 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.342105 |
| Step 2 | 19.33908 |
| Step 3 | 19.33908 |
After 3 steps the estimate is 19.33908, matching √374 ≈ 19.33908.
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Frequently asked questions
Is 374 a perfect square?
No, 374 is not a perfect square, so its square root is irrational and approximately 19.33908.
What is the square root of 374 in simplest radical form?
√374 = √374 in simplest radical form.