Square Root Calculator › Square root of 316
Square Root of 316
√316 ≈ 17.776389
316 is not a perfect square, so √316 is an irrational number that is approximately 17.776389. In simplified radical form, √316 = 2√79.
√316 lies between √289 = 17 and √324 = 18.
| Number | 316 |
| Square root (decimal) | 17.776389 |
| Simplified radical | 2√79 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 316
316 = 2^2 × 79. This is what determines the simplified radical: for √316 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √316 = 2√79.
Estimating √316 by hand
√316 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 316 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.794118 |
| Step 2 | 17.776398 |
| Step 3 | 17.776389 |
After 3 steps the estimate is 17.776389, matching √316 ≈ 17.776389.
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Frequently asked questions
Is 316 a perfect square?
No, 316 is not a perfect square, so its square root is irrational and approximately 17.776389.
What is the square root of 316 in simplest radical form?
√316 = 2√79 in simplest radical form.