Square Root Calculator › Square root of 131
Square Root of 131
√131 ≈ 11.445523
131 is not a perfect square, so √131 is an irrational number that is approximately 11.445523. In simplified radical form, √131 = √131.
√131 lies between √121 = 11 and √144 = 12.
| Number | 131 |
| Square root (decimal) | 11.445523 |
| Simplified radical | √131 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 131
131 = 131. This is what determines the simplified radical: for √131 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √131 is already in simplest radical form as √131.
Estimating √131 by hand
√131 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 131 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.454545 |
| Step 2 | 11.445527 |
| Step 3 | 11.445523 |
After 3 steps the estimate is 11.445523, matching √131 ≈ 11.445523.
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Frequently asked questions
Is 131 a perfect square?
No, 131 is not a perfect square, so its square root is irrational and approximately 11.445523.
What is the square root of 131 in simplest radical form?
√131 = √131 in simplest radical form.