Square Root Calculator › Square root of 297
Square Root of 297
√297 ≈ 17.233688
297 is not a perfect square, so √297 is an irrational number that is approximately 17.233688. In simplified radical form, √297 = 3√33.
√297 lies between √289 = 17 and √324 = 18.
| Number | 297 |
| Square root (decimal) | 17.233688 |
| Simplified radical | 3√33 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 297
297 = 3^3 × 11. This is what determines the simplified radical: for √297 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √297 = 3√33.
Estimating √297 by hand
√297 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 297 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.235294 |
| Step 2 | 17.233688 |
| Step 3 | 17.233688 |
After 3 steps the estimate is 17.233688, matching √297 ≈ 17.233688.
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Frequently asked questions
Is 297 a perfect square?
No, 297 is not a perfect square, so its square root is irrational and approximately 17.233688.
What is the square root of 297 in simplest radical form?
√297 = 3√33 in simplest radical form.