Square Root Calculator › Square root of 145
Square Root of 145
√145 ≈ 12.041595
145 is not a perfect square, so √145 is an irrational number that is approximately 12.041595. In simplified radical form, √145 = √145.
√145 lies between √144 = 12 and √169 = 13.
| Number | 145 |
| Square root (decimal) | 12.041595 |
| Simplified radical | √145 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 145
145 = 5 × 29. This is what determines the simplified radical: for √145 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √145 is already in simplest radical form as √145.
Estimating √145 by hand
√145 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 145 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.041667 |
| Step 2 | 12.041595 |
| Step 3 | 12.041595 |
After 3 steps the estimate is 12.041595, matching √145 ≈ 12.041595.
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Frequently asked questions
Is 145 a perfect square?
No, 145 is not a perfect square, so its square root is irrational and approximately 12.041595.
What is the square root of 145 in simplest radical form?
√145 = √145 in simplest radical form.