Square Root Calculator › Square root of 338
Square Root of 338
√338 ≈ 18.384776
338 is not a perfect square, so √338 is an irrational number that is approximately 18.384776. In simplified radical form, √338 = 13√2.
√338 lies between √324 = 18 and √361 = 19.
| Number | 338 |
| Square root (decimal) | 18.384776 |
| Simplified radical | 13√2 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 338
338 = 2 × 13^2. This is what determines the simplified radical: for √338 you pull out one copy of any prime that appears twice.
Here the paired factor 13 comes out from under the root, leaving √338 = 13√2.
Estimating √338 by hand
√338 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 338 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.388889 |
| Step 2 | 18.384777 |
| Step 3 | 18.384776 |
After 3 steps the estimate is 18.384776, matching √338 ≈ 18.384776.
Nearby square roots
Frequently asked questions
Is 338 a perfect square?
No, 338 is not a perfect square, so its square root is irrational and approximately 18.384776.
What is the square root of 338 in simplest radical form?
√338 = 13√2 in simplest radical form.