Square Root Calculator › Square root of 176
Square Root of 176
√176 ≈ 13.266499
176 is not a perfect square, so √176 is an irrational number that is approximately 13.266499. In simplified radical form, √176 = 4√11.
√176 lies between √169 = 13 and √196 = 14.
| Number | 176 |
| Square root (decimal) | 13.266499 |
| Simplified radical | 4√11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 176
176 = 2^4 × 11. This is what determines the simplified radical: for √176 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √176 = 4√11.
Estimating √176 by hand
√176 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 176 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.269231 |
| Step 2 | 13.266499 |
| Step 3 | 13.266499 |
After 3 steps the estimate is 13.266499, matching √176 ≈ 13.266499.
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Frequently asked questions
Is 176 a perfect square?
No, 176 is not a perfect square, so its square root is irrational and approximately 13.266499.
What is the square root of 176 in simplest radical form?
√176 = 4√11 in simplest radical form.