Square Root Calculator › Square root of 540
Square Root of 540
√540 ≈ 23.2379
540 is not a perfect square, so √540 is an irrational number that is approximately 23.2379. In simplified radical form, √540 = 6√15.
√540 lies between √529 = 23 and √576 = 24.
| Number | 540 |
| Square root (decimal) | 23.2379 |
| Simplified radical | 6√15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 540
540 = 2^2 × 3^3 × 5. This is what determines the simplified radical: for √540 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √540 = 6√15.
Estimating √540 by hand
√540 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 540 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.23913 |
| Step 2 | 23.2379 |
| Step 3 | 23.2379 |
After 3 steps the estimate is 23.2379, matching √540 ≈ 23.2379.
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Frequently asked questions
Is 540 a perfect square?
No, 540 is not a perfect square, so its square root is irrational and approximately 23.2379.
What is the square root of 540 in simplest radical form?
√540 = 6√15 in simplest radical form.