Square Root Calculator › Square root of 184
Square Root of 184
√184 ≈ 13.56466
184 is not a perfect square, so √184 is an irrational number that is approximately 13.56466. In simplified radical form, √184 = 2√46.
√184 lies between √169 = 13 and √196 = 14.
| Number | 184 |
| Square root (decimal) | 13.56466 |
| Simplified radical | 2√46 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 184
184 = 2^3 × 23. This is what determines the simplified radical: for √184 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √184 = 2√46.
Estimating √184 by hand
√184 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 184 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.576923 |
| Step 2 | 13.564666 |
| Step 3 | 13.56466 |
After 3 steps the estimate is 13.56466, matching √184 ≈ 13.56466.
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Frequently asked questions
Is 184 a perfect square?
No, 184 is not a perfect square, so its square root is irrational and approximately 13.56466.
What is the square root of 184 in simplest radical form?
√184 = 2√46 in simplest radical form.