Square Root Calculator › Square root of 328
Square Root of 328
√328 ≈ 18.11077
328 is not a perfect square, so √328 is an irrational number that is approximately 18.11077. In simplified radical form, √328 = 2√82.
√328 lies between √324 = 18 and √361 = 19.
| Number | 328 |
| Square root (decimal) | 18.11077 |
| Simplified radical | 2√82 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 328
328 = 2^3 × 41. This is what determines the simplified radical: for √328 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √328 = 2√82.
Estimating √328 by hand
√328 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 328 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.111111 |
| Step 2 | 18.11077 |
| Step 3 | 18.11077 |
After 3 steps the estimate is 18.11077, matching √328 ≈ 18.11077.
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Frequently asked questions
Is 328 a perfect square?
No, 328 is not a perfect square, so its square root is irrational and approximately 18.11077.
What is the square root of 328 in simplest radical form?
√328 = 2√82 in simplest radical form.