Square Root Calculator › Square root of 347
Square Root of 347
√347 ≈ 18.627936
347 is not a perfect square, so √347 is an irrational number that is approximately 18.627936. In simplified radical form, √347 = √347.
√347 lies between √324 = 18 and √361 = 19.
| Number | 347 |
| Square root (decimal) | 18.627936 |
| Simplified radical | √347 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 347
347 = 347. This is what determines the simplified radical: for √347 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √347 is already in simplest radical form as √347.
Estimating √347 by hand
√347 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 347 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.638889 |
| Step 2 | 18.627939 |
| Step 3 | 18.627936 |
After 3 steps the estimate is 18.627936, matching √347 ≈ 18.627936.
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Frequently asked questions
Is 347 a perfect square?
No, 347 is not a perfect square, so its square root is irrational and approximately 18.627936.
What is the square root of 347 in simplest radical form?
√347 = √347 in simplest radical form.