Square Root Calculator › Square root of 141
Square Root of 141
√141 ≈ 11.874342
141 is not a perfect square, so √141 is an irrational number that is approximately 11.874342. In simplified radical form, √141 = √141.
√141 lies between √121 = 11 and √144 = 12.
| Number | 141 |
| Square root (decimal) | 11.874342 |
| Simplified radical | √141 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 141
141 = 3 × 47. This is what determines the simplified radical: for √141 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √141 is already in simplest radical form as √141.
Estimating √141 by hand
√141 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 141 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.909091 |
| Step 2 | 11.874393 |
| Step 3 | 11.874342 |
After 3 steps the estimate is 11.874342, matching √141 ≈ 11.874342.
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Frequently asked questions
Is 141 a perfect square?
No, 141 is not a perfect square, so its square root is irrational and approximately 11.874342.
What is the square root of 141 in simplest radical form?
√141 = √141 in simplest radical form.