Square Root Calculator › Square root of 317
Square Root of 317
√317 ≈ 17.804494
317 is not a perfect square, so √317 is an irrational number that is approximately 17.804494. In simplified radical form, √317 = √317.
√317 lies between √289 = 17 and √324 = 18.
| Number | 317 |
| Square root (decimal) | 17.804494 |
| Simplified radical | √317 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 317
317 = 317. This is what determines the simplified radical: for √317 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √317 is already in simplest radical form as √317.
Estimating √317 by hand
√317 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 317 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.823529 |
| Step 2 | 17.804504 |
| Step 3 | 17.804494 |
After 3 steps the estimate is 17.804494, matching √317 ≈ 17.804494.
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Frequently asked questions
Is 317 a perfect square?
No, 317 is not a perfect square, so its square root is irrational and approximately 17.804494.
What is the square root of 317 in simplest radical form?
√317 = √317 in simplest radical form.