Square Root Calculator › Square root of 536
Square Root of 536
√536 ≈ 23.151674
536 is not a perfect square, so √536 is an irrational number that is approximately 23.151674. In simplified radical form, √536 = 2√134.
√536 lies between √529 = 23 and √576 = 24.
| Number | 536 |
| Square root (decimal) | 23.151674 |
| Simplified radical | 2√134 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 536
536 = 2^3 × 67. This is what determines the simplified radical: for √536 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √536 = 2√134.
Estimating √536 by hand
√536 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 536 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.152174 |
| Step 2 | 23.151674 |
| Step 3 | 23.151674 |
After 3 steps the estimate is 23.151674, matching √536 ≈ 23.151674.
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Frequently asked questions
Is 536 a perfect square?
No, 536 is not a perfect square, so its square root is irrational and approximately 23.151674.
What is the square root of 536 in simplest radical form?
√536 = 2√134 in simplest radical form.