Square Root Calculator › Square root of 159
Square Root of 159
√159 ≈ 12.60952
159 is not a perfect square, so √159 is an irrational number that is approximately 12.60952. In simplified radical form, √159 = √159.
√159 lies between √144 = 12 and √169 = 13.
| Number | 159 |
| Square root (decimal) | 12.60952 |
| Simplified radical | √159 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 159
159 = 3 × 53. This is what determines the simplified radical: for √159 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √159 is already in simplest radical form as √159.
Estimating √159 by hand
√159 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 159 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.625 |
| Step 2 | 12.60953 |
| Step 3 | 12.60952 |
After 3 steps the estimate is 12.60952, matching √159 ≈ 12.60952.
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Frequently asked questions
Is 159 a perfect square?
No, 159 is not a perfect square, so its square root is irrational and approximately 12.60952.
What is the square root of 159 in simplest radical form?
√159 = √159 in simplest radical form.