Square Root Calculator › Square root of 562
Square Root of 562
√562 ≈ 23.706539
562 is not a perfect square, so √562 is an irrational number that is approximately 23.706539. In simplified radical form, √562 = √562.
√562 lies between √529 = 23 and √576 = 24.
| Number | 562 |
| Square root (decimal) | 23.706539 |
| Simplified radical | √562 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 562
562 = 2 × 281. This is what determines the simplified radical: for √562 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √562 is already in simplest radical form as √562.
Estimating √562 by hand
√562 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 562 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.717391 |
| Step 2 | 23.706542 |
| Step 3 | 23.706539 |
After 3 steps the estimate is 23.706539, matching √562 ≈ 23.706539.
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Frequently asked questions
Is 562 a perfect square?
No, 562 is not a perfect square, so its square root is irrational and approximately 23.706539.
What is the square root of 562 in simplest radical form?
√562 = √562 in simplest radical form.