Square Root Calculator › Square root of 156
Square Root of 156
√156 ≈ 12.489996
156 is not a perfect square, so √156 is an irrational number that is approximately 12.489996. In simplified radical form, √156 = 2√39.
√156 lies between √144 = 12 and √169 = 13.
| Number | 156 |
| Square root (decimal) | 12.489996 |
| Simplified radical | 2√39 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 156
156 = 2^2 × 3 × 13. This is what determines the simplified radical: for √156 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √156 = 2√39.
Estimating √156 by hand
√156 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 156 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.5 |
| Step 2 | 12.49 |
| Step 3 | 12.489996 |
After 3 steps the estimate is 12.489996, matching √156 ≈ 12.489996.
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Frequently asked questions
Is 156 a perfect square?
No, 156 is not a perfect square, so its square root is irrational and approximately 12.489996.
What is the square root of 156 in simplest radical form?
√156 = 2√39 in simplest radical form.