Square Root Calculator › Square root of 318
Square Root of 318
√318 ≈ 17.832555
318 is not a perfect square, so √318 is an irrational number that is approximately 17.832555. In simplified radical form, √318 = √318.
√318 lies between √289 = 17 and √324 = 18.
| Number | 318 |
| Square root (decimal) | 17.832555 |
| Simplified radical | √318 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 318
318 = 2 × 3 × 53. This is what determines the simplified radical: for √318 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √318 is already in simplest radical form as √318.
Estimating √318 by hand
√318 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 318 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.852941 |
| Step 2 | 17.832566 |
| Step 3 | 17.832555 |
After 3 steps the estimate is 17.832555, matching √318 ≈ 17.832555.
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Frequently asked questions
Is 318 a perfect square?
No, 318 is not a perfect square, so its square root is irrational and approximately 17.832555.
What is the square root of 318 in simplest radical form?
√318 = √318 in simplest radical form.