Square Root Calculator › Square root of 108
Square Root of 108
√108 ≈ 10.392305
108 is not a perfect square, so √108 is an irrational number that is approximately 10.392305. In simplified radical form, √108 = 6√3.
√108 lies between √100 = 10 and √121 = 11.
| Number | 108 |
| Square root (decimal) | 10.392305 |
| Simplified radical | 6√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 108
108 = 2^2 × 3^3. This is what determines the simplified radical: for √108 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √108 = 6√3.
Estimating √108 by hand
√108 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 108 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.4 |
| Step 2 | 10.392308 |
| Step 3 | 10.392305 |
After 3 steps the estimate is 10.392305, matching √108 ≈ 10.392305.
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Frequently asked questions
Is 108 a perfect square?
No, 108 is not a perfect square, so its square root is irrational and approximately 10.392305.
What is the square root of 108 in simplest radical form?
√108 = 6√3 in simplest radical form.