Square Root Calculator › Square root of 114
Square Root of 114
√114 ≈ 10.677078
114 is not a perfect square, so √114 is an irrational number that is approximately 10.677078. In simplified radical form, √114 = √114.
√114 lies between √100 = 10 and √121 = 11.
| Number | 114 |
| Square root (decimal) | 10.677078 |
| Simplified radical | √114 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 114
114 = 2 × 3 × 19. This is what determines the simplified radical: for √114 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √114 is already in simplest radical form as √114.
Estimating √114 by hand
√114 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 114 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.7 |
| Step 2 | 10.677103 |
| Step 3 | 10.677078 |
After 3 steps the estimate is 10.677078, matching √114 ≈ 10.677078.
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Frequently asked questions
Is 114 a perfect square?
No, 114 is not a perfect square, so its square root is irrational and approximately 10.677078.
What is the square root of 114 in simplest radical form?
√114 = √114 in simplest radical form.