Square Root Calculator › Square root of 143
Square Root of 143
√143 ≈ 11.958261
143 is not a perfect square, so √143 is an irrational number that is approximately 11.958261. In simplified radical form, √143 = √143.
√143 lies between √121 = 11 and √144 = 12.
| Number | 143 |
| Square root (decimal) | 11.958261 |
| Simplified radical | √143 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 143
143 = 11 × 13. This is what determines the simplified radical: for √143 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √143 is already in simplest radical form as √143.
Estimating √143 by hand
√143 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 143 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 12 |
| Step 2 | 11.958333 |
| Step 3 | 11.958261 |
After 3 steps the estimate is 11.958261, matching √143 ≈ 11.958261.
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Frequently asked questions
Is 143 a perfect square?
No, 143 is not a perfect square, so its square root is irrational and approximately 11.958261.
What is the square root of 143 in simplest radical form?
√143 = √143 in simplest radical form.