Square Root Calculator › Square root of 314
Square Root of 314
√314 ≈ 17.720045
314 is not a perfect square, so √314 is an irrational number that is approximately 17.720045. In simplified radical form, √314 = √314.
√314 lies between √289 = 17 and √324 = 18.
| Number | 314 |
| Square root (decimal) | 17.720045 |
| Simplified radical | √314 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 314
314 = 2 × 157. This is what determines the simplified radical: for √314 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √314 is already in simplest radical form as √314.
Estimating √314 by hand
√314 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 314 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.735294 |
| Step 2 | 17.720052 |
| Step 3 | 17.720045 |
After 3 steps the estimate is 17.720045, matching √314 ≈ 17.720045.
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Frequently asked questions
Is 314 a perfect square?
No, 314 is not a perfect square, so its square root is irrational and approximately 17.720045.
What is the square root of 314 in simplest radical form?
√314 = √314 in simplest radical form.