Square Root Calculator › Square root of 491
Square Root of 491
√491 ≈ 22.15852
491 is not a perfect square, so √491 is an irrational number that is approximately 22.15852. In simplified radical form, √491 = √491.
√491 lies between √484 = 22 and √529 = 23.
| Number | 491 |
| Square root (decimal) | 22.15852 |
| Simplified radical | √491 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 491
491 = 491. This is what determines the simplified radical: for √491 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √491 is already in simplest radical form as √491.
Estimating √491 by hand
√491 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 491 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.159091 |
| Step 2 | 22.15852 |
| Step 3 | 22.15852 |
After 3 steps the estimate is 22.15852, matching √491 ≈ 22.15852.
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Frequently asked questions
Is 491 a perfect square?
No, 491 is not a perfect square, so its square root is irrational and approximately 22.15852.
What is the square root of 491 in simplest radical form?
√491 = √491 in simplest radical form.