Square Root Calculator › Square root of 125
Square Root of 125
√125 ≈ 11.18034
125 is not a perfect square, so √125 is an irrational number that is approximately 11.18034. In simplified radical form, √125 = 5√5.
√125 lies between √121 = 11 and √144 = 12.
| Number | 125 |
| Square root (decimal) | 11.18034 |
| Simplified radical | 5√5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 125
125 = 5^3. This is what determines the simplified radical: for √125 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √125 = 5√5.
Estimating √125 by hand
√125 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 125 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.181818 |
| Step 2 | 11.18034 |
| Step 3 | 11.18034 |
After 3 steps the estimate is 11.18034, matching √125 ≈ 11.18034.
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Frequently asked questions
Is 125 a perfect square?
No, 125 is not a perfect square, so its square root is irrational and approximately 11.18034.
What is the square root of 125 in simplest radical form?
√125 = 5√5 in simplest radical form.