Square Root Calculator › Square root of 248
Square Root of 248
√248 ≈ 15.748016
248 is not a perfect square, so √248 is an irrational number that is approximately 15.748016. In simplified radical form, √248 = 2√62.
√248 lies between √225 = 15 and √256 = 16.
| Number | 248 |
| Square root (decimal) | 15.748016 |
| Simplified radical | 2√62 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 248
248 = 2^3 × 31. This is what determines the simplified radical: for √248 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √248 = 2√62.
Estimating √248 by hand
√248 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 248 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.766667 |
| Step 2 | 15.748027 |
| Step 3 | 15.748016 |
After 3 steps the estimate is 15.748016, matching √248 ≈ 15.748016.
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Frequently asked questions
Is 248 a perfect square?
No, 248 is not a perfect square, so its square root is irrational and approximately 15.748016.
What is the square root of 248 in simplest radical form?
√248 = 2√62 in simplest radical form.