Square Root Calculator › Square root of 326
Square Root of 326
√326 ≈ 18.05547
326 is not a perfect square, so √326 is an irrational number that is approximately 18.05547. In simplified radical form, √326 = √326.
√326 lies between √324 = 18 and √361 = 19.
| Number | 326 |
| Square root (decimal) | 18.05547 |
| Simplified radical | √326 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 326
326 = 2 × 163. This is what determines the simplified radical: for √326 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √326 is already in simplest radical form as √326.
Estimating √326 by hand
√326 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 326 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.055556 |
| Step 2 | 18.05547 |
| Step 3 | 18.05547 |
After 3 steps the estimate is 18.05547, matching √326 ≈ 18.05547.
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Frequently asked questions
Is 326 a perfect square?
No, 326 is not a perfect square, so its square root is irrational and approximately 18.05547.
What is the square root of 326 in simplest radical form?
√326 = √326 in simplest radical form.