Square Root Calculator › Square root of 308
Square Root of 308
√308 ≈ 17.549929
308 is not a perfect square, so √308 is an irrational number that is approximately 17.549929. In simplified radical form, √308 = 2√77.
√308 lies between √289 = 17 and √324 = 18.
| Number | 308 |
| Square root (decimal) | 17.549929 |
| Simplified radical | 2√77 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 308
308 = 2^2 × 7 × 11. This is what determines the simplified radical: for √308 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √308 = 2√77.
Estimating √308 by hand
√308 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 308 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.558824 |
| Step 2 | 17.549931 |
| Step 3 | 17.549929 |
After 3 steps the estimate is 17.549929, matching √308 ≈ 17.549929.
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Frequently asked questions
Is 308 a perfect square?
No, 308 is not a perfect square, so its square root is irrational and approximately 17.549929.
What is the square root of 308 in simplest radical form?
√308 = 2√77 in simplest radical form.