Square Root Calculator › Square root of 292
Square Root of 292
√292 ≈ 17.088007
292 is not a perfect square, so √292 is an irrational number that is approximately 17.088007. In simplified radical form, √292 = 2√73.
√292 lies between √289 = 17 and √324 = 18.
| Number | 292 |
| Square root (decimal) | 17.088007 |
| Simplified radical | 2√73 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 292
292 = 2^2 × 73. This is what determines the simplified radical: for √292 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √292 = 2√73.
Estimating √292 by hand
√292 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 292 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.088235 |
| Step 2 | 17.088007 |
| Step 3 | 17.088007 |
After 3 steps the estimate is 17.088007, matching √292 ≈ 17.088007.
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Frequently asked questions
Is 292 a perfect square?
No, 292 is not a perfect square, so its square root is irrational and approximately 17.088007.
What is the square root of 292 in simplest radical form?
√292 = 2√73 in simplest radical form.