Square Root Calculator › Square root of 535
Square Root of 535
√535 ≈ 23.130067
535 is not a perfect square, so √535 is an irrational number that is approximately 23.130067. In simplified radical form, √535 = √535.
√535 lies between √529 = 23 and √576 = 24.
| Number | 535 |
| Square root (decimal) | 23.130067 |
| Simplified radical | √535 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 535
535 = 5 × 107. This is what determines the simplified radical: for √535 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √535 is already in simplest radical form as √535.
Estimating √535 by hand
√535 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 535 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.130435 |
| Step 2 | 23.130067 |
| Step 3 | 23.130067 |
After 3 steps the estimate is 23.130067, matching √535 ≈ 23.130067.
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Frequently asked questions
Is 535 a perfect square?
No, 535 is not a perfect square, so its square root is irrational and approximately 23.130067.
What is the square root of 535 in simplest radical form?
√535 = √535 in simplest radical form.