Square Root Calculator › Square root of 296
Square Root of 296
√296 ≈ 17.204651
296 is not a perfect square, so √296 is an irrational number that is approximately 17.204651. In simplified radical form, √296 = 2√74.
√296 lies between √289 = 17 and √324 = 18.
| Number | 296 |
| Square root (decimal) | 17.204651 |
| Simplified radical | 2√74 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 296
296 = 2^3 × 37. This is what determines the simplified radical: for √296 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √296 = 2√74.
Estimating √296 by hand
√296 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 296 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.205882 |
| Step 2 | 17.204651 |
| Step 3 | 17.204651 |
After 3 steps the estimate is 17.204651, matching √296 ≈ 17.204651.
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Frequently asked questions
Is 296 a perfect square?
No, 296 is not a perfect square, so its square root is irrational and approximately 17.204651.
What is the square root of 296 in simplest radical form?
√296 = 2√74 in simplest radical form.