Square Root Calculator › Square root of 603
Square Root of 603
√603 ≈ 24.556058
603 is not a perfect square, so √603 is an irrational number that is approximately 24.556058. In simplified radical form, √603 = 3√67.
√603 lies between √576 = 24 and √625 = 25.
| Number | 603 |
| Square root (decimal) | 24.556058 |
| Simplified radical | 3√67 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 603
603 = 3^2 × 67. This is what determines the simplified radical: for √603 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √603 = 3√67.
Estimating √603 by hand
√603 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 603 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.5625 |
| Step 2 | 24.556059 |
| Step 3 | 24.556058 |
After 3 steps the estimate is 24.556058, matching √603 ≈ 24.556058.
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Frequently asked questions
Is 603 a perfect square?
No, 603 is not a perfect square, so its square root is irrational and approximately 24.556058.
What is the square root of 603 in simplest radical form?
√603 = 3√67 in simplest radical form.