Square Root Calculator › Square root of 273
Square Root of 273
√273 ≈ 16.522712
273 is not a perfect square, so √273 is an irrational number that is approximately 16.522712. In simplified radical form, √273 = √273.
√273 lies between √256 = 16 and √289 = 17.
| Number | 273 |
| Square root (decimal) | 16.522712 |
| Simplified radical | √273 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 273
273 = 3 × 7 × 13. This is what determines the simplified radical: for √273 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √273 is already in simplest radical form as √273.
Estimating √273 by hand
√273 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 273 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.53125 |
| Step 2 | 16.522714 |
| Step 3 | 16.522712 |
After 3 steps the estimate is 16.522712, matching √273 ≈ 16.522712.
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Frequently asked questions
Is 273 a perfect square?
No, 273 is not a perfect square, so its square root is irrational and approximately 16.522712.
What is the square root of 273 in simplest radical form?
√273 = √273 in simplest radical form.