Square Root Calculator › Square root of 322
Square Root of 322
√322 ≈ 17.944358
322 is not a perfect square, so √322 is an irrational number that is approximately 17.944358. In simplified radical form, √322 = √322.
√322 lies between √289 = 17 and √324 = 18.
| Number | 322 |
| Square root (decimal) | 17.944358 |
| Simplified radical | √322 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 322
322 = 2 × 7 × 23. This is what determines the simplified radical: for √322 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √322 is already in simplest radical form as √322.
Estimating √322 by hand
√322 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 322 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.970588 |
| Step 2 | 17.944378 |
| Step 3 | 17.944358 |
After 3 steps the estimate is 17.944358, matching √322 ≈ 17.944358.
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Frequently asked questions
Is 322 a perfect square?
No, 322 is not a perfect square, so its square root is irrational and approximately 17.944358.
What is the square root of 322 in simplest radical form?
√322 = √322 in simplest radical form.