Square Root Calculator › Square root of 362
Square Root of 362
√362 ≈ 19.026298
362 is not a perfect square, so √362 is an irrational number that is approximately 19.026298. In simplified radical form, √362 = √362.
√362 lies between √361 = 19 and √400 = 20.
| Number | 362 |
| Square root (decimal) | 19.026298 |
| Simplified radical | √362 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 362
362 = 2 × 181. This is what determines the simplified radical: for √362 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √362 is already in simplest radical form as √362.
Estimating √362 by hand
√362 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 362 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.026316 |
| Step 2 | 19.026298 |
| Step 3 | 19.026298 |
After 3 steps the estimate is 19.026298, matching √362 ≈ 19.026298.
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Frequently asked questions
Is 362 a perfect square?
No, 362 is not a perfect square, so its square root is irrational and approximately 19.026298.
What is the square root of 362 in simplest radical form?
√362 = √362 in simplest radical form.