Square Root Calculator › Square root of 274
Square Root of 274
√274 ≈ 16.552945
274 is not a perfect square, so √274 is an irrational number that is approximately 16.552945. In simplified radical form, √274 = √274.
√274 lies between √256 = 16 and √289 = 17.
| Number | 274 |
| Square root (decimal) | 16.552945 |
| Simplified radical | √274 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 274
274 = 2 × 137. This is what determines the simplified radical: for √274 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √274 is already in simplest radical form as √274.
Estimating √274 by hand
√274 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 274 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.5625 |
| Step 2 | 16.552948 |
| Step 3 | 16.552945 |
After 3 steps the estimate is 16.552945, matching √274 ≈ 16.552945.
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Frequently asked questions
Is 274 a perfect square?
No, 274 is not a perfect square, so its square root is irrational and approximately 16.552945.
What is the square root of 274 in simplest radical form?
√274 = √274 in simplest radical form.