Square Root Calculator › Square root of 146
Square Root of 146
√146 ≈ 12.083046
146 is not a perfect square, so √146 is an irrational number that is approximately 12.083046. In simplified radical form, √146 = √146.
√146 lies between √144 = 12 and √169 = 13.
| Number | 146 |
| Square root (decimal) | 12.083046 |
| Simplified radical | √146 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 146
146 = 2 × 73. This is what determines the simplified radical: for √146 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √146 is already in simplest radical form as √146.
Estimating √146 by hand
√146 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 146 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.083333 |
| Step 2 | 12.083046 |
| Step 3 | 12.083046 |
After 3 steps the estimate is 12.083046, matching √146 ≈ 12.083046.
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Frequently asked questions
Is 146 a perfect square?
No, 146 is not a perfect square, so its square root is irrational and approximately 12.083046.
What is the square root of 146 in simplest radical form?
√146 = √146 in simplest radical form.