Square Root Calculator › Square root of 359
Square Root of 359
√359 ≈ 18.947295
359 is not a perfect square, so √359 is an irrational number that is approximately 18.947295. In simplified radical form, √359 = √359.
√359 lies between √324 = 18 and √361 = 19.
| Number | 359 |
| Square root (decimal) | 18.947295 |
| Simplified radical | √359 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 359
359 = 359. This is what determines the simplified radical: for √359 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √359 is already in simplest radical form as √359.
Estimating √359 by hand
√359 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 359 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.972222 |
| Step 2 | 18.947312 |
| Step 3 | 18.947295 |
After 3 steps the estimate is 18.947295, matching √359 ≈ 18.947295.
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Frequently asked questions
Is 359 a perfect square?
No, 359 is not a perfect square, so its square root is irrational and approximately 18.947295.
What is the square root of 359 in simplest radical form?
√359 = √359 in simplest radical form.