Square Root Calculator › Square root of 542
Square Root of 542
√542 ≈ 23.280893
542 is not a perfect square, so √542 is an irrational number that is approximately 23.280893. In simplified radical form, √542 = √542.
√542 lies between √529 = 23 and √576 = 24.
| Number | 542 |
| Square root (decimal) | 23.280893 |
| Simplified radical | √542 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 542
542 = 2 × 271. This is what determines the simplified radical: for √542 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √542 is already in simplest radical form as √542.
Estimating √542 by hand
√542 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 542 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.282609 |
| Step 2 | 23.280894 |
| Step 3 | 23.280893 |
After 3 steps the estimate is 23.280893, matching √542 ≈ 23.280893.
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Frequently asked questions
Is 542 a perfect square?
No, 542 is not a perfect square, so its square root is irrational and approximately 23.280893.
What is the square root of 542 in simplest radical form?
√542 = √542 in simplest radical form.