Square Root Calculator › Square root of 373
Square Root of 373
√373 ≈ 19.313208
373 is not a perfect square, so √373 is an irrational number that is approximately 19.313208. In simplified radical form, √373 = √373.
√373 lies between √361 = 19 and √400 = 20.
| Number | 373 |
| Square root (decimal) | 19.313208 |
| Simplified radical | √373 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 373
373 = 373. This is what determines the simplified radical: for √373 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √373 is already in simplest radical form as √373.
Estimating √373 by hand
√373 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 373 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.315789 |
| Step 2 | 19.313208 |
| Step 3 | 19.313208 |
After 3 steps the estimate is 19.313208, matching √373 ≈ 19.313208.
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Frequently asked questions
Is 373 a perfect square?
No, 373 is not a perfect square, so its square root is irrational and approximately 19.313208.
What is the square root of 373 in simplest radical form?
√373 = √373 in simplest radical form.