Square Root Calculator › Square root of 116
Square Root of 116
√116 ≈ 10.77033
116 is not a perfect square, so √116 is an irrational number that is approximately 10.77033. In simplified radical form, √116 = 2√29.
√116 lies between √100 = 10 and √121 = 11.
| Number | 116 |
| Square root (decimal) | 10.77033 |
| Simplified radical | 2√29 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 116
116 = 2^2 × 29. This is what determines the simplified radical: for √116 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √116 = 2√29.
Estimating √116 by hand
√116 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 116 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.8 |
| Step 2 | 10.77037 |
| Step 3 | 10.77033 |
After 3 steps the estimate is 10.77033, matching √116 ≈ 10.77033.
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Frequently asked questions
Is 116 a perfect square?
No, 116 is not a perfect square, so its square root is irrational and approximately 10.77033.
What is the square root of 116 in simplest radical form?
√116 = 2√29 in simplest radical form.