Square Root Calculator › Square root of 122
Square Root of 122
√122 ≈ 11.045361
122 is not a perfect square, so √122 is an irrational number that is approximately 11.045361. In simplified radical form, √122 = √122.
√122 lies between √121 = 11 and √144 = 12.
| Number | 122 |
| Square root (decimal) | 11.045361 |
| Simplified radical | √122 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 122
122 = 2 × 61. This is what determines the simplified radical: for √122 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √122 is already in simplest radical form as √122.
Estimating √122 by hand
√122 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 122 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.045455 |
| Step 2 | 11.045361 |
| Step 3 | 11.045361 |
After 3 steps the estimate is 11.045361, matching √122 ≈ 11.045361.
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Frequently asked questions
Is 122 a perfect square?
No, 122 is not a perfect square, so its square root is irrational and approximately 11.045361.
What is the square root of 122 in simplest radical form?
√122 = √122 in simplest radical form.