Square Root Calculator › Square root of 110
Square Root of 110
√110 ≈ 10.488088
110 is not a perfect square, so √110 is an irrational number that is approximately 10.488088. In simplified radical form, √110 = √110.
√110 lies between √100 = 10 and √121 = 11.
| Number | 110 |
| Square root (decimal) | 10.488088 |
| Simplified radical | √110 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 110
110 = 2 × 5 × 11. This is what determines the simplified radical: for √110 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √110 is already in simplest radical form as √110.
Estimating √110 by hand
√110 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 110 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.5 |
| Step 2 | 10.488095 |
| Step 3 | 10.488088 |
After 3 steps the estimate is 10.488088, matching √110 ≈ 10.488088.
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Frequently asked questions
Is 110 a perfect square?
No, 110 is not a perfect square, so its square root is irrational and approximately 10.488088.
What is the square root of 110 in simplest radical form?
√110 = √110 in simplest radical form.