Square Root Calculator › Square root of 152
Square Root of 152
√152 ≈ 12.328828
152 is not a perfect square, so √152 is an irrational number that is approximately 12.328828. In simplified radical form, √152 = 2√38.
√152 lies between √144 = 12 and √169 = 13.
| Number | 152 |
| Square root (decimal) | 12.328828 |
| Simplified radical | 2√38 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 152
152 = 2^3 × 19. This is what determines the simplified radical: for √152 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √152 = 2√38.
Estimating √152 by hand
√152 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 152 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.333333 |
| Step 2 | 12.328829 |
| Step 3 | 12.328828 |
After 3 steps the estimate is 12.328828, matching √152 ≈ 12.328828.
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Frequently asked questions
Is 152 a perfect square?
No, 152 is not a perfect square, so its square root is irrational and approximately 12.328828.
What is the square root of 152 in simplest radical form?
√152 = 2√38 in simplest radical form.