Square Root Calculator › Square root of 346
Square Root of 346
√346 ≈ 18.601075
346 is not a perfect square, so √346 is an irrational number that is approximately 18.601075. In simplified radical form, √346 = √346.
√346 lies between √324 = 18 and √361 = 19.
| Number | 346 |
| Square root (decimal) | 18.601075 |
| Simplified radical | √346 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 346
346 = 2 × 173. This is what determines the simplified radical: for √346 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √346 is already in simplest radical form as √346.
Estimating √346 by hand
√346 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 346 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.611111 |
| Step 2 | 18.601078 |
| Step 3 | 18.601075 |
After 3 steps the estimate is 18.601075, matching √346 ≈ 18.601075.
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Frequently asked questions
Is 346 a perfect square?
No, 346 is not a perfect square, so its square root is irrational and approximately 18.601075.
What is the square root of 346 in simplest radical form?
√346 = √346 in simplest radical form.