Square Root Calculator › Square root of 294
Square Root of 294
√294 ≈ 17.146428
294 is not a perfect square, so √294 is an irrational number that is approximately 17.146428. In simplified radical form, √294 = 7√6.
√294 lies between √289 = 17 and √324 = 18.
| Number | 294 |
| Square root (decimal) | 17.146428 |
| Simplified radical | 7√6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 294
294 = 2 × 3 × 7^2. This is what determines the simplified radical: for √294 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √294 = 7√6.
Estimating √294 by hand
√294 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 294 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.147059 |
| Step 2 | 17.146428 |
| Step 3 | 17.146428 |
After 3 steps the estimate is 17.146428, matching √294 ≈ 17.146428.
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Frequently asked questions
Is 294 a perfect square?
No, 294 is not a perfect square, so its square root is irrational and approximately 17.146428.
What is the square root of 294 in simplest radical form?
√294 = 7√6 in simplest radical form.