Square Root Calculator › Square root of 124
Square Root of 124
√124 ≈ 11.135529
124 is not a perfect square, so √124 is an irrational number that is approximately 11.135529. In simplified radical form, √124 = 2√31.
√124 lies between √121 = 11 and √144 = 12.
| Number | 124 |
| Square root (decimal) | 11.135529 |
| Simplified radical | 2√31 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 124
124 = 2^2 × 31. This is what determines the simplified radical: for √124 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √124 = 2√31.
Estimating √124 by hand
√124 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 124 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.136364 |
| Step 2 | 11.135529 |
| Step 3 | 11.135529 |
After 3 steps the estimate is 11.135529, matching √124 ≈ 11.135529.
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Frequently asked questions
Is 124 a perfect square?
No, 124 is not a perfect square, so its square root is irrational and approximately 11.135529.
What is the square root of 124 in simplest radical form?
√124 = 2√31 in simplest radical form.