Square Root Calculator › Square root of 344
Square Root of 344
√344 ≈ 18.547237
344 is not a perfect square, so √344 is an irrational number that is approximately 18.547237. In simplified radical form, √344 = 2√86.
√344 lies between √324 = 18 and √361 = 19.
| Number | 344 |
| Square root (decimal) | 18.547237 |
| Simplified radical | 2√86 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 344
344 = 2^3 × 43. This is what determines the simplified radical: for √344 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √344 = 2√86.
Estimating √344 by hand
√344 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 344 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.555556 |
| Step 2 | 18.547239 |
| Step 3 | 18.547237 |
After 3 steps the estimate is 18.547237, matching √344 ≈ 18.547237.
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Frequently asked questions
Is 344 a perfect square?
No, 344 is not a perfect square, so its square root is irrational and approximately 18.547237.
What is the square root of 344 in simplest radical form?
√344 = 2√86 in simplest radical form.