Square Root Calculator › Square root of 301
Square Root of 301
√301 ≈ 17.349352
301 is not a perfect square, so √301 is an irrational number that is approximately 17.349352. In simplified radical form, √301 = √301.
√301 lies between √289 = 17 and √324 = 18.
| Number | 301 |
| Square root (decimal) | 17.349352 |
| Simplified radical | √301 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 301
301 = 7 × 43. This is what determines the simplified radical: for √301 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √301 is already in simplest radical form as √301.
Estimating √301 by hand
√301 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 301 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.352941 |
| Step 2 | 17.349352 |
| Step 3 | 17.349352 |
After 3 steps the estimate is 17.349352, matching √301 ≈ 17.349352.
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Frequently asked questions
Is 301 a perfect square?
No, 301 is not a perfect square, so its square root is irrational and approximately 17.349352.
What is the square root of 301 in simplest radical form?
√301 = √301 in simplest radical form.