Square Root Calculator › Square root of 588
Square Root of 588
√588 ≈ 24.248711
588 is not a perfect square, so √588 is an irrational number that is approximately 24.248711. In simplified radical form, √588 = 14√3.
√588 lies between √576 = 24 and √625 = 25.
| Number | 588 |
| Square root (decimal) | 24.248711 |
| Simplified radical | 14√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 588
588 = 2^2 × 3 × 7^2. This is what determines the simplified radical: for √588 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 7 come out from under the root, leaving √588 = 14√3.
Estimating √588 by hand
√588 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 588 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.25 |
| Step 2 | 24.248711 |
| Step 3 | 24.248711 |
After 3 steps the estimate is 24.248711, matching √588 ≈ 24.248711.
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Frequently asked questions
Is 588 a perfect square?
No, 588 is not a perfect square, so its square root is irrational and approximately 24.248711.
What is the square root of 588 in simplest radical form?
√588 = 14√3 in simplest radical form.