Square Root Calculator › Square root of 293
Square Root of 293
√293 ≈ 17.117243
293 is not a perfect square, so √293 is an irrational number that is approximately 17.117243. In simplified radical form, √293 = √293.
√293 lies between √289 = 17 and √324 = 18.
| Number | 293 |
| Square root (decimal) | 17.117243 |
| Simplified radical | √293 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 293
293 = 293. This is what determines the simplified radical: for √293 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √293 is already in simplest radical form as √293.
Estimating √293 by hand
√293 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 293 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.117647 |
| Step 2 | 17.117243 |
| Step 3 | 17.117243 |
After 3 steps the estimate is 17.117243, matching √293 ≈ 17.117243.
Nearby square roots
Frequently asked questions
Is 293 a perfect square?
No, 293 is not a perfect square, so its square root is irrational and approximately 17.117243.
What is the square root of 293 in simplest radical form?
√293 = √293 in simplest radical form.