Square Root Calculator › Square root of 118
Square Root of 118
√118 ≈ 10.86278
118 is not a perfect square, so √118 is an irrational number that is approximately 10.86278. In simplified radical form, √118 = √118.
√118 lies between √100 = 10 and √121 = 11.
| Number | 118 |
| Square root (decimal) | 10.86278 |
| Simplified radical | √118 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 118
118 = 2 × 59. This is what determines the simplified radical: for √118 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √118 is already in simplest radical form as √118.
Estimating √118 by hand
√118 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 118 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.9 |
| Step 2 | 10.862844 |
| Step 3 | 10.86278 |
After 3 steps the estimate is 10.86278, matching √118 ≈ 10.86278.
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Frequently asked questions
Is 118 a perfect square?
No, 118 is not a perfect square, so its square root is irrational and approximately 10.86278.
What is the square root of 118 in simplest radical form?
√118 = √118 in simplest radical form.