Square Root Calculator › Square root of 158
Square Root of 158
√158 ≈ 12.569805
158 is not a perfect square, so √158 is an irrational number that is approximately 12.569805. In simplified radical form, √158 = √158.
√158 lies between √144 = 12 and √169 = 13.
| Number | 158 |
| Square root (decimal) | 12.569805 |
| Simplified radical | √158 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 158
158 = 2 × 79. This is what determines the simplified radical: for √158 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √158 is already in simplest radical form as √158.
Estimating √158 by hand
√158 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 158 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.583333 |
| Step 2 | 12.569812 |
| Step 3 | 12.569805 |
After 3 steps the estimate is 12.569805, matching √158 ≈ 12.569805.
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Frequently asked questions
Is 158 a perfect square?
No, 158 is not a perfect square, so its square root is irrational and approximately 12.569805.
What is the square root of 158 in simplest radical form?
√158 = √158 in simplest radical form.