Square Root Calculator › Square root of 348
Square Root of 348
√348 ≈ 18.654758
348 is not a perfect square, so √348 is an irrational number that is approximately 18.654758. In simplified radical form, √348 = 2√87.
√348 lies between √324 = 18 and √361 = 19.
| Number | 348 |
| Square root (decimal) | 18.654758 |
| Simplified radical | 2√87 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 348
348 = 2^2 × 3 × 29. This is what determines the simplified radical: for √348 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √348 = 2√87.
Estimating √348 by hand
√348 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 348 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.666667 |
| Step 2 | 18.654762 |
| Step 3 | 18.654758 |
After 3 steps the estimate is 18.654758, matching √348 ≈ 18.654758.
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Frequently asked questions
Is 348 a perfect square?
No, 348 is not a perfect square, so its square root is irrational and approximately 18.654758.
What is the square root of 348 in simplest radical form?
√348 = 2√87 in simplest radical form.