Square Root Calculator › Square root of 534
Square Root of 534
√534 ≈ 23.10844
534 is not a perfect square, so √534 is an irrational number that is approximately 23.10844. In simplified radical form, √534 = √534.
√534 lies between √529 = 23 and √576 = 24.
| Number | 534 |
| Square root (decimal) | 23.10844 |
| Simplified radical | √534 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 534
534 = 2 × 3 × 89. This is what determines the simplified radical: for √534 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √534 is already in simplest radical form as √534.
Estimating √534 by hand
√534 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 534 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.108696 |
| Step 2 | 23.10844 |
| Step 3 | 23.10844 |
After 3 steps the estimate is 23.10844, matching √534 ≈ 23.10844.
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Frequently asked questions
Is 534 a perfect square?
No, 534 is not a perfect square, so its square root is irrational and approximately 23.10844.
What is the square root of 534 in simplest radical form?
√534 = √534 in simplest radical form.