Square Root Calculator › Square root of 247
Square Root of 247
√247 ≈ 15.716234
247 is not a perfect square, so √247 is an irrational number that is approximately 15.716234. In simplified radical form, √247 = √247.
√247 lies between √225 = 15 and √256 = 16.
| Number | 247 |
| Square root (decimal) | 15.716234 |
| Simplified radical | √247 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 247
247 = 13 × 19. This is what determines the simplified radical: for √247 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √247 is already in simplest radical form as √247.
Estimating √247 by hand
√247 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 247 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.733333 |
| Step 2 | 15.716243 |
| Step 3 | 15.716234 |
After 3 steps the estimate is 15.716234, matching √247 ≈ 15.716234.
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Frequently asked questions
Is 247 a perfect square?
No, 247 is not a perfect square, so its square root is irrational and approximately 15.716234.
What is the square root of 247 in simplest radical form?
√247 = √247 in simplest radical form.