Square Root Calculator › Square root of 323
Square Root of 323
√323 ≈ 17.972201
323 is not a perfect square, so √323 is an irrational number that is approximately 17.972201. In simplified radical form, √323 = √323.
√323 lies between √289 = 17 and √324 = 18.
| Number | 323 |
| Square root (decimal) | 17.972201 |
| Simplified radical | √323 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 323
323 = 17 × 19. This is what determines the simplified radical: for √323 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √323 is already in simplest radical form as √323.
Estimating √323 by hand
√323 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 323 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 18 |
| Step 2 | 17.972222 |
| Step 3 | 17.972201 |
After 3 steps the estimate is 17.972201, matching √323 ≈ 17.972201.
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Frequently asked questions
Is 323 a perfect square?
No, 323 is not a perfect square, so its square root is irrational and approximately 17.972201.
What is the square root of 323 in simplest radical form?
√323 = √323 in simplest radical form.