Square Root Calculator › Square root of 575
Square Root of 575
√575 ≈ 23.979158
575 is not a perfect square, so √575 is an irrational number that is approximately 23.979158. In simplified radical form, √575 = 5√23.
√575 lies between √529 = 23 and √576 = 24.
| Number | 575 |
| Square root (decimal) | 23.979158 |
| Simplified radical | 5√23 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 575
575 = 5^2 × 23. This is what determines the simplified radical: for √575 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √575 = 5√23.
Estimating √575 by hand
√575 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 575 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 24 |
| Step 2 | 23.979167 |
| Step 3 | 23.979158 |
After 3 steps the estimate is 23.979158, matching √575 ≈ 23.979158.
Nearby square roots
Frequently asked questions
Is 575 a perfect square?
No, 575 is not a perfect square, so its square root is irrational and approximately 23.979158.
What is the square root of 575 in simplest radical form?
√575 = 5√23 in simplest radical form.