Square Root Calculator › Square root of 94
Square Root of 94
√94 ≈ 9.69536
94 is not a perfect square, so √94 is an irrational number that is approximately 9.69536. In simplified radical form, √94 = √94.
√94 lies between √81 = 9 and √100 = 10.
| Number | 94 |
| Square root (decimal) | 9.69536 |
| Simplified radical | √94 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 94
94 = 2 × 47. This is what determines the simplified radical: for √94 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √94 is already in simplest radical form as √94.
Estimating √94 by hand
√94 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 94 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.722222 |
| Step 2 | 9.695397 |
| Step 3 | 9.69536 |
After 3 steps the estimate is 9.69536, matching √94 ≈ 9.69536.
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Frequently asked questions
Is 94 a perfect square?
No, 94 is not a perfect square, so its square root is irrational and approximately 9.69536.
What is the square root of 94 in simplest radical form?
√94 = √94 in simplest radical form.