Square Root Calculator › Square root of 591
Square Root of 591
√591 ≈ 24.310492
591 is not a perfect square, so √591 is an irrational number that is approximately 24.310492. In simplified radical form, √591 = √591.
√591 lies between √576 = 24 and √625 = 25.
| Number | 591 |
| Square root (decimal) | 24.310492 |
| Simplified radical | √591 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 591
591 = 3 × 197. This is what determines the simplified radical: for √591 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √591 is already in simplest radical form as √591.
Estimating √591 by hand
√591 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 591 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.3125 |
| Step 2 | 24.310492 |
| Step 3 | 24.310492 |
After 3 steps the estimate is 24.310492, matching √591 ≈ 24.310492.
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Frequently asked questions
Is 591 a perfect square?
No, 591 is not a perfect square, so its square root is irrational and approximately 24.310492.
What is the square root of 591 in simplest radical form?
√591 = √591 in simplest radical form.