Square Root Calculator › Square root of 140
Square Root of 140
√140 ≈ 11.83216
140 is not a perfect square, so √140 is an irrational number that is approximately 11.83216. In simplified radical form, √140 = 2√35.
√140 lies between √121 = 11 and √144 = 12.
| Number | 140 |
| Square root (decimal) | 11.83216 |
| Simplified radical | 2√35 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 140
140 = 2^2 × 5 × 7. This is what determines the simplified radical: for √140 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √140 = 2√35.
Estimating √140 by hand
√140 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 140 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.863636 |
| Step 2 | 11.832201 |
| Step 3 | 11.83216 |
After 3 steps the estimate is 11.83216, matching √140 ≈ 11.83216.
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Frequently asked questions
Is 140 a perfect square?
No, 140 is not a perfect square, so its square root is irrational and approximately 11.83216.
What is the square root of 140 in simplest radical form?
√140 = 2√35 in simplest radical form.