Square Root Calculator › Square root of 334
Square Root of 334
√334 ≈ 18.275667
334 is not a perfect square, so √334 is an irrational number that is approximately 18.275667. In simplified radical form, √334 = √334.
√334 lies between √324 = 18 and √361 = 19.
| Number | 334 |
| Square root (decimal) | 18.275667 |
| Simplified radical | √334 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 334
334 = 2 × 167. This is what determines the simplified radical: for √334 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √334 is already in simplest radical form as √334.
Estimating √334 by hand
√334 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 334 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.277778 |
| Step 2 | 18.275667 |
| Step 3 | 18.275667 |
After 3 steps the estimate is 18.275667, matching √334 ≈ 18.275667.
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Frequently asked questions
Is 334 a perfect square?
No, 334 is not a perfect square, so its square root is irrational and approximately 18.275667.
What is the square root of 334 in simplest radical form?
√334 = √334 in simplest radical form.