Square Root Calculator › Square root of 245
Square Root of 245
√245 ≈ 15.652476
245 is not a perfect square, so √245 is an irrational number that is approximately 15.652476. In simplified radical form, √245 = 7√5.
√245 lies between √225 = 15 and √256 = 16.
| Number | 245 |
| Square root (decimal) | 15.652476 |
| Simplified radical | 7√5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 245
245 = 5 × 7^2. This is what determines the simplified radical: for √245 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √245 = 7√5.
Estimating √245 by hand
√245 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 245 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.666667 |
| Step 2 | 15.652482 |
| Step 3 | 15.652476 |
After 3 steps the estimate is 15.652476, matching √245 ≈ 15.652476.
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Frequently asked questions
Is 245 a perfect square?
No, 245 is not a perfect square, so its square root is irrational and approximately 15.652476.
What is the square root of 245 in simplest radical form?
√245 = 7√5 in simplest radical form.