Square Root Calculator › Square root of 252
Square Root of 252
√252 ≈ 15.874508
252 is not a perfect square, so √252 is an irrational number that is approximately 15.874508. In simplified radical form, √252 = 6√7.
√252 lies between √225 = 15 and √256 = 16.
| Number | 252 |
| Square root (decimal) | 15.874508 |
| Simplified radical | 6√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 252
252 = 2^2 × 3^2 × 7. This is what determines the simplified radical: for √252 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √252 = 6√7.
Estimating √252 by hand
√252 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 252 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.9 |
| Step 2 | 15.874528 |
| Step 3 | 15.874508 |
After 3 steps the estimate is 15.874508, matching √252 ≈ 15.874508.
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Frequently asked questions
Is 252 a perfect square?
No, 252 is not a perfect square, so its square root is irrational and approximately 15.874508.
What is the square root of 252 in simplest radical form?
√252 = 6√7 in simplest radical form.