Square Root Calculator › Square root of 253
Square Root of 253
√253 ≈ 15.905974
253 is not a perfect square, so √253 is an irrational number that is approximately 15.905974. In simplified radical form, √253 = √253.
√253 lies between √225 = 15 and √256 = 16.
| Number | 253 |
| Square root (decimal) | 15.905974 |
| Simplified radical | √253 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 253
253 = 11 × 23. This is what determines the simplified radical: for √253 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √253 is already in simplest radical form as √253.
Estimating √253 by hand
√253 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 253 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.933333 |
| Step 2 | 15.905997 |
| Step 3 | 15.905974 |
After 3 steps the estimate is 15.905974, matching √253 ≈ 15.905974.
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Frequently asked questions
Is 253 a perfect square?
No, 253 is not a perfect square, so its square root is irrational and approximately 15.905974.
What is the square root of 253 in simplest radical form?
√253 = √253 in simplest radical form.