Square Root Calculator › Square root of 291
Square Root of 291
√291 ≈ 17.058722
291 is not a perfect square, so √291 is an irrational number that is approximately 17.058722. In simplified radical form, √291 = √291.
√291 lies between √289 = 17 and √324 = 18.
| Number | 291 |
| Square root (decimal) | 17.058722 |
| Simplified radical | √291 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 291
291 = 3 × 97. This is what determines the simplified radical: for √291 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √291 is already in simplest radical form as √291.
Estimating √291 by hand
√291 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 291 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.058824 |
| Step 2 | 17.058722 |
| Step 3 | 17.058722 |
After 3 steps the estimate is 17.058722, matching √291 ≈ 17.058722.
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Frequently asked questions
Is 291 a perfect square?
No, 291 is not a perfect square, so its square root is irrational and approximately 17.058722.
What is the square root of 291 in simplest radical form?
√291 = √291 in simplest radical form.