Square Root Calculator › Square root of 299
Square Root of 299
√299 ≈ 17.291616
299 is not a perfect square, so √299 is an irrational number that is approximately 17.291616. In simplified radical form, √299 = √299.
√299 lies between √289 = 17 and √324 = 18.
| Number | 299 |
| Square root (decimal) | 17.291616 |
| Simplified radical | √299 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 299
299 = 13 × 23. This is what determines the simplified radical: for √299 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √299 is already in simplest radical form as √299.
Estimating √299 by hand
√299 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 299 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.294118 |
| Step 2 | 17.291617 |
| Step 3 | 17.291616 |
After 3 steps the estimate is 17.291616, matching √299 ≈ 17.291616.
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Frequently asked questions
Is 299 a perfect square?
No, 299 is not a perfect square, so its square root is irrational and approximately 17.291616.
What is the square root of 299 in simplest radical form?
√299 = √299 in simplest radical form.