Square Root Calculator › Square root of 179
Square Root of 179
√179 ≈ 13.379088
179 is not a perfect square, so √179 is an irrational number that is approximately 13.379088. In simplified radical form, √179 = √179.
√179 lies between √169 = 13 and √196 = 14.
| Number | 179 |
| Square root (decimal) | 13.379088 |
| Simplified radical | √179 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 179
179 = 179. This is what determines the simplified radical: for √179 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √179 is already in simplest radical form as √179.
Estimating √179 by hand
√179 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 179 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.384615 |
| Step 2 | 13.379089 |
| Step 3 | 13.379088 |
After 3 steps the estimate is 13.379088, matching √179 ≈ 13.379088.
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Frequently asked questions
Is 179 a perfect square?
No, 179 is not a perfect square, so its square root is irrational and approximately 13.379088.
What is the square root of 179 in simplest radical form?
√179 = √179 in simplest radical form.