Square Root Calculator › Square root of 548
Square Root of 548
√548 ≈ 23.4094
548 is not a perfect square, so √548 is an irrational number that is approximately 23.4094. In simplified radical form, √548 = 2√137.
√548 lies between √529 = 23 and √576 = 24.
| Number | 548 |
| Square root (decimal) | 23.4094 |
| Simplified radical | 2√137 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 548
548 = 2^2 × 137. This is what determines the simplified radical: for √548 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √548 = 2√137.
Estimating √548 by hand
√548 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 548 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.413043 |
| Step 2 | 23.4094 |
| Step 3 | 23.4094 |
After 3 steps the estimate is 23.4094, matching √548 ≈ 23.4094.
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Frequently asked questions
Is 548 a perfect square?
No, 548 is not a perfect square, so its square root is irrational and approximately 23.4094.
What is the square root of 548 in simplest radical form?
√548 = 2√137 in simplest radical form.