Square Root Calculator › Square root of 142
Square Root of 142
√142 ≈ 11.916375
142 is not a perfect square, so √142 is an irrational number that is approximately 11.916375. In simplified radical form, √142 = √142.
√142 lies between √121 = 11 and √144 = 12.
| Number | 142 |
| Square root (decimal) | 11.916375 |
| Simplified radical | √142 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 142
142 = 2 × 71. This is what determines the simplified radical: for √142 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √142 is already in simplest radical form as √142.
Estimating √142 by hand
√142 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 142 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.954545 |
| Step 2 | 11.916436 |
| Step 3 | 11.916375 |
After 3 steps the estimate is 11.916375, matching √142 ≈ 11.916375.
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Frequently asked questions
Is 142 a perfect square?
No, 142 is not a perfect square, so its square root is irrational and approximately 11.916375.
What is the square root of 142 in simplest radical form?
√142 = √142 in simplest radical form.