Square Root Calculator › Square root of 325
Square Root of 325
√325 ≈ 18.027756
325 is not a perfect square, so √325 is an irrational number that is approximately 18.027756. In simplified radical form, √325 = 5√13.
√325 lies between √324 = 18 and √361 = 19.
| Number | 325 |
| Square root (decimal) | 18.027756 |
| Simplified radical | 5√13 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 325
325 = 5^2 × 13. This is what determines the simplified radical: for √325 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √325 = 5√13.
Estimating √325 by hand
√325 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 325 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.027778 |
| Step 2 | 18.027756 |
| Step 3 | 18.027756 |
After 3 steps the estimate is 18.027756, matching √325 ≈ 18.027756.
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Frequently asked questions
Is 325 a perfect square?
No, 325 is not a perfect square, so its square root is irrational and approximately 18.027756.
What is the square root of 325 in simplest radical form?
√325 = 5√13 in simplest radical form.