Square Root Calculator › Square root of 149
Square Root of 149
√149 ≈ 12.206556
149 is not a perfect square, so √149 is an irrational number that is approximately 12.206556. In simplified radical form, √149 = √149.
√149 lies between √144 = 12 and √169 = 13.
| Number | 149 |
| Square root (decimal) | 12.206556 |
| Simplified radical | √149 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 149
149 = 149. This is what determines the simplified radical: for √149 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √149 is already in simplest radical form as √149.
Estimating √149 by hand
√149 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 149 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.208333 |
| Step 2 | 12.206556 |
| Step 3 | 12.206556 |
After 3 steps the estimate is 12.206556, matching √149 ≈ 12.206556.
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Frequently asked questions
Is 149 a perfect square?
No, 149 is not a perfect square, so its square root is irrational and approximately 12.206556.
What is the square root of 149 in simplest radical form?
√149 = √149 in simplest radical form.