Square Root Calculator › Square root of 92
Square Root of 92
√92 ≈ 9.591663
92 is not a perfect square, so √92 is an irrational number that is approximately 9.591663. In simplified radical form, √92 = 2√23.
√92 lies between √81 = 9 and √100 = 10.
| Number | 92 |
| Square root (decimal) | 9.591663 |
| Simplified radical | 2√23 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 92
92 = 2^2 × 23. This is what determines the simplified radical: for √92 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √92 = 2√23.
Estimating √92 by hand
√92 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 92 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.611111 |
| Step 2 | 9.591683 |
| Step 3 | 9.591663 |
After 3 steps the estimate is 9.591663, matching √92 ≈ 9.591663.
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Frequently asked questions
Is 92 a perfect square?
No, 92 is not a perfect square, so its square root is irrational and approximately 9.591663.
What is the square root of 92 in simplest radical form?
√92 = 2√23 in simplest radical form.