Square Root Calculator › Square root of 543
Square Root of 543
√543 ≈ 23.30236
543 is not a perfect square, so √543 is an irrational number that is approximately 23.30236. In simplified radical form, √543 = √543.
√543 lies between √529 = 23 and √576 = 24.
| Number | 543 |
| Square root (decimal) | 23.30236 |
| Simplified radical | √543 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 543
543 = 3 × 181. This is what determines the simplified radical: for √543 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √543 is already in simplest radical form as √543.
Estimating √543 by hand
√543 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 543 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.304348 |
| Step 2 | 23.30236 |
| Step 3 | 23.30236 |
After 3 steps the estimate is 23.30236, matching √543 ≈ 23.30236.
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Frequently asked questions
Is 543 a perfect square?
No, 543 is not a perfect square, so its square root is irrational and approximately 23.30236.
What is the square root of 543 in simplest radical form?
√543 = √543 in simplest radical form.