Square Root Calculator › Square root of 315
Square Root of 315
√315 ≈ 17.748239
315 is not a perfect square, so √315 is an irrational number that is approximately 17.748239. In simplified radical form, √315 = 3√35.
√315 lies between √289 = 17 and √324 = 18.
| Number | 315 |
| Square root (decimal) | 17.748239 |
| Simplified radical | 3√35 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 315
315 = 3^2 × 5 × 7. This is what determines the simplified radical: for √315 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √315 = 3√35.
Estimating √315 by hand
√315 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 315 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.764706 |
| Step 2 | 17.748247 |
| Step 3 | 17.748239 |
After 3 steps the estimate is 17.748239, matching √315 ≈ 17.748239.
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Frequently asked questions
Is 315 a perfect square?
No, 315 is not a perfect square, so its square root is irrational and approximately 17.748239.
What is the square root of 315 in simplest radical form?
√315 = 3√35 in simplest radical form.