Square Root Calculator › Square root of 546
Square Root of 546
√546 ≈ 23.366643
546 is not a perfect square, so √546 is an irrational number that is approximately 23.366643. In simplified radical form, √546 = √546.
√546 lies between √529 = 23 and √576 = 24.
| Number | 546 |
| Square root (decimal) | 23.366643 |
| Simplified radical | √546 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 546
546 = 2 × 3 × 7 × 13. This is what determines the simplified radical: for √546 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √546 is already in simplest radical form as √546.
Estimating √546 by hand
√546 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 546 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.369565 |
| Step 2 | 23.366643 |
| Step 3 | 23.366643 |
After 3 steps the estimate is 23.366643, matching √546 ≈ 23.366643.
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Frequently asked questions
Is 546 a perfect square?
No, 546 is not a perfect square, so its square root is irrational and approximately 23.366643.
What is the square root of 546 in simplest radical form?
√546 = √546 in simplest radical form.