Square Root Calculator › Square root of 526
Square Root of 526
√526 ≈ 22.93469
526 is not a perfect square, so √526 is an irrational number that is approximately 22.93469. In simplified radical form, √526 = √526.
√526 lies between √484 = 22 and √529 = 23.
| Number | 526 |
| Square root (decimal) | 22.93469 |
| Simplified radical | √526 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 526
526 = 2 × 263. This is what determines the simplified radical: for √526 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √526 is already in simplest radical form as √526.
Estimating √526 by hand
√526 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 526 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.954545 |
| Step 2 | 22.934698 |
| Step 3 | 22.93469 |
After 3 steps the estimate is 22.93469, matching √526 ≈ 22.93469.
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Frequently asked questions
Is 526 a perfect square?
No, 526 is not a perfect square, so its square root is irrational and approximately 22.93469.
What is the square root of 526 in simplest radical form?
√526 = √526 in simplest radical form.