Square Root Calculator › Square root of 97
Square Root of 97
√97 ≈ 9.848858
97 is not a perfect square, so √97 is an irrational number that is approximately 9.848858. In simplified radical form, √97 = √97.
√97 lies between √81 = 9 and √100 = 10.
| Number | 97 |
| Square root (decimal) | 9.848858 |
| Simplified radical | √97 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 97
97 = 97. This is what determines the simplified radical: for √97 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √97 is already in simplest radical form as √97.
Estimating √97 by hand
√97 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 97 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.888889 |
| Step 2 | 9.848939 |
| Step 3 | 9.848858 |
After 3 steps the estimate is 9.848858, matching √97 ≈ 9.848858.
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Frequently asked questions
Is 97 a perfect square?
No, 97 is not a perfect square, so its square root is irrational and approximately 9.848858.
What is the square root of 97 in simplest radical form?
√97 = √97 in simplest radical form.