Square Root Calculator › Square root of 54
Square Root of 54
√54 ≈ 7.348469
54 is not a perfect square, so √54 is an irrational number that is approximately 7.348469. In simplified radical form, √54 = 3√6.
√54 lies between √49 = 7 and √64 = 8.
| Number | 54 |
| Square root (decimal) | 7.348469 |
| Simplified radical | 3√6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 54
54 = 2 × 3^3. This is what determines the simplified radical: for √54 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √54 = 3√6.
Estimating √54 by hand
√54 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 54 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.357143 |
| Step 2 | 7.348474 |
| Step 3 | 7.348469 |
After 3 steps the estimate is 7.348469, matching √54 ≈ 7.348469.
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Frequently asked questions
Is 54 a perfect square?
No, 54 is not a perfect square, so its square root is irrational and approximately 7.348469.
What is the square root of 54 in simplest radical form?
√54 = 3√6 in simplest radical form.