Square Root Calculator › Square root of 120
Square Root of 120
√120 ≈ 10.954451
120 is not a perfect square, so √120 is an irrational number that is approximately 10.954451. In simplified radical form, √120 = 2√30.
√120 lies between √100 = 10 and √121 = 11.
| Number | 120 |
| Square root (decimal) | 10.954451 |
| Simplified radical | 2√30 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 120
120 = 2^3 × 3 × 5. This is what determines the simplified radical: for √120 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √120 = 2√30.
Estimating √120 by hand
√120 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 120 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 11 |
| Step 2 | 10.954545 |
| Step 3 | 10.954451 |
After 3 steps the estimate is 10.954451, matching √120 ≈ 10.954451.
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Frequently asked questions
Is 120 a perfect square?
No, 120 is not a perfect square, so its square root is irrational and approximately 10.954451.
What is the square root of 120 in simplest radical form?
√120 = 2√30 in simplest radical form.