Square Root Calculator › Square root of 298
Square Root of 298
√298 ≈ 17.262677
298 is not a perfect square, so √298 is an irrational number that is approximately 17.262677. In simplified radical form, √298 = √298.
√298 lies between √289 = 17 and √324 = 18.
| Number | 298 |
| Square root (decimal) | 17.262677 |
| Simplified radical | √298 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 298
298 = 2 × 149. This is what determines the simplified radical: for √298 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √298 is already in simplest radical form as √298.
Estimating √298 by hand
√298 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 298 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.264706 |
| Step 2 | 17.262677 |
| Step 3 | 17.262677 |
After 3 steps the estimate is 17.262677, matching √298 ≈ 17.262677.
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Frequently asked questions
Is 298 a perfect square?
No, 298 is not a perfect square, so its square root is irrational and approximately 17.262677.
What is the square root of 298 in simplest radical form?
√298 = √298 in simplest radical form.