Square Root Calculator › Square root of 91
Square Root of 91
√91 ≈ 9.539392
91 is not a perfect square, so √91 is an irrational number that is approximately 9.539392. In simplified radical form, √91 = √91.
√91 lies between √81 = 9 and √100 = 10.
| Number | 91 |
| Square root (decimal) | 9.539392 |
| Simplified radical | √91 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 91
91 = 7 × 13. This is what determines the simplified radical: for √91 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √91 is already in simplest radical form as √91.
Estimating √91 by hand
√91 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 91 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.555556 |
| Step 2 | 9.539406 |
| Step 3 | 9.539392 |
After 3 steps the estimate is 9.539392, matching √91 ≈ 9.539392.
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Frequently asked questions
Is 91 a perfect square?
No, 91 is not a perfect square, so its square root is irrational and approximately 9.539392.
What is the square root of 91 in simplest radical form?
√91 = √91 in simplest radical form.