Square Root Calculator › Square root of 541
Square Root of 541
√541 ≈ 23.259407
541 is not a perfect square, so √541 is an irrational number that is approximately 23.259407. In simplified radical form, √541 = √541.
√541 lies between √529 = 23 and √576 = 24.
| Number | 541 |
| Square root (decimal) | 23.259407 |
| Simplified radical | √541 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 541
541 = 541. This is what determines the simplified radical: for √541 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √541 is already in simplest radical form as √541.
Estimating √541 by hand
√541 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 541 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.26087 |
| Step 2 | 23.259407 |
| Step 3 | 23.259407 |
After 3 steps the estimate is 23.259407, matching √541 ≈ 23.259407.
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Frequently asked questions
Is 541 a perfect square?
No, 541 is not a perfect square, so its square root is irrational and approximately 23.259407.
What is the square root of 541 in simplest radical form?
√541 = √541 in simplest radical form.