Square Root Calculator › Square root of 367
Square Root of 367
√367 ≈ 19.157244
367 is not a perfect square, so √367 is an irrational number that is approximately 19.157244. In simplified radical form, √367 = √367.
√367 lies between √361 = 19 and √400 = 20.
| Number | 367 |
| Square root (decimal) | 19.157244 |
| Simplified radical | √367 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 367
367 = 367. This is what determines the simplified radical: for √367 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √367 is already in simplest radical form as √367.
Estimating √367 by hand
√367 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 367 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.157895 |
| Step 2 | 19.157244 |
| Step 3 | 19.157244 |
After 3 steps the estimate is 19.157244, matching √367 ≈ 19.157244.
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Frequently asked questions
Is 367 a perfect square?
No, 367 is not a perfect square, so its square root is irrational and approximately 19.157244.
What is the square root of 367 in simplest radical form?
√367 = √367 in simplest radical form.