Square Root Calculator › Square root of 545
Square Root of 545
√545 ≈ 23.345235
545 is not a perfect square, so √545 is an irrational number that is approximately 23.345235. In simplified radical form, √545 = √545.
√545 lies between √529 = 23 and √576 = 24.
| Number | 545 |
| Square root (decimal) | 23.345235 |
| Simplified radical | √545 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 545
545 = 5 × 109. This is what determines the simplified radical: for √545 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √545 is already in simplest radical form as √545.
Estimating √545 by hand
√545 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 545 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.347826 |
| Step 2 | 23.345235 |
| Step 3 | 23.345235 |
After 3 steps the estimate is 23.345235, matching √545 ≈ 23.345235.
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Frequently asked questions
Is 545 a perfect square?
No, 545 is not a perfect square, so its square root is irrational and approximately 23.345235.
What is the square root of 545 in simplest radical form?
√545 = √545 in simplest radical form.