Square Root Calculator › Square root of 366
Square Root of 366
√366 ≈ 19.131126
366 is not a perfect square, so √366 is an irrational number that is approximately 19.131126. In simplified radical form, √366 = √366.
√366 lies between √361 = 19 and √400 = 20.
| Number | 366 |
| Square root (decimal) | 19.131126 |
| Simplified radical | √366 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 366
366 = 2 × 3 × 61. This is what determines the simplified radical: for √366 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √366 is already in simplest radical form as √366.
Estimating √366 by hand
√366 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 366 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.131579 |
| Step 2 | 19.131126 |
| Step 3 | 19.131126 |
After 3 steps the estimate is 19.131126, matching √366 ≈ 19.131126.
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Frequently asked questions
Is 366 a perfect square?
No, 366 is not a perfect square, so its square root is irrational and approximately 19.131126.
What is the square root of 366 in simplest radical form?
√366 = √366 in simplest radical form.