Square Root Calculator › Square root of 115
Square Root of 115
√115 ≈ 10.723805
115 is not a perfect square, so √115 is an irrational number that is approximately 10.723805. In simplified radical form, √115 = √115.
√115 lies between √100 = 10 and √121 = 11.
| Number | 115 |
| Square root (decimal) | 10.723805 |
| Simplified radical | √115 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 115
115 = 5 × 23. This is what determines the simplified radical: for √115 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √115 is already in simplest radical form as √115.
Estimating √115 by hand
√115 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 115 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.75 |
| Step 2 | 10.723837 |
| Step 3 | 10.723805 |
After 3 steps the estimate is 10.723805, matching √115 ≈ 10.723805.
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Frequently asked questions
Is 115 a perfect square?
No, 115 is not a perfect square, so its square root is irrational and approximately 10.723805.
What is the square root of 115 in simplest radical form?
√115 = √115 in simplest radical form.