Square Root Calculator › Square root of 93
Square Root of 93
√93 ≈ 9.643651
93 is not a perfect square, so √93 is an irrational number that is approximately 9.643651. In simplified radical form, √93 = √93.
√93 lies between √81 = 9 and √100 = 10.
| Number | 93 |
| Square root (decimal) | 9.643651 |
| Simplified radical | √93 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 93
93 = 3 × 31. This is what determines the simplified radical: for √93 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √93 is already in simplest radical form as √93.
Estimating √93 by hand
√93 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 93 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.666667 |
| Step 2 | 9.643678 |
| Step 3 | 9.643651 |
After 3 steps the estimate is 9.643651, matching √93 ≈ 9.643651.
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Frequently asked questions
Is 93 a perfect square?
No, 93 is not a perfect square, so its square root is irrational and approximately 9.643651.
What is the square root of 93 in simplest radical form?
√93 = √93 in simplest radical form.