Square Root Calculator › Square root of 182
Square Root of 182
√182 ≈ 13.490738
182 is not a perfect square, so √182 is an irrational number that is approximately 13.490738. In simplified radical form, √182 = √182.
√182 lies between √169 = 13 and √196 = 14.
| Number | 182 |
| Square root (decimal) | 13.490738 |
| Simplified radical | √182 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 182
182 = 2 × 7 × 13. This is what determines the simplified radical: for √182 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √182 is already in simplest radical form as √182.
Estimating √182 by hand
√182 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 182 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.5 |
| Step 2 | 13.490741 |
| Step 3 | 13.490738 |
After 3 steps the estimate is 13.490738, matching √182 ≈ 13.490738.
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Frequently asked questions
Is 182 a perfect square?
No, 182 is not a perfect square, so its square root is irrational and approximately 13.490738.
What is the square root of 182 in simplest radical form?
√182 = √182 in simplest radical form.