Square Root Calculator › Square root of 183
Square Root of 183
√183 ≈ 13.527749
183 is not a perfect square, so √183 is an irrational number that is approximately 13.527749. In simplified radical form, √183 = √183.
√183 lies between √169 = 13 and √196 = 14.
| Number | 183 |
| Square root (decimal) | 13.527749 |
| Simplified radical | √183 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 183
183 = 3 × 61. This is what determines the simplified radical: for √183 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √183 is already in simplest radical form as √183.
Estimating √183 by hand
√183 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 183 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.538462 |
| Step 2 | 13.527753 |
| Step 3 | 13.527749 |
After 3 steps the estimate is 13.527749, matching √183 ≈ 13.527749.
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Frequently asked questions
Is 183 a perfect square?
No, 183 is not a perfect square, so its square root is irrational and approximately 13.527749.
What is the square root of 183 in simplest radical form?
√183 = √183 in simplest radical form.