Square Root Calculator › Square root of 304
Square Root of 304
√304 ≈ 17.435596
304 is not a perfect square, so √304 is an irrational number that is approximately 17.435596. In simplified radical form, √304 = 4√19.
√304 lies between √289 = 17 and √324 = 18.
| Number | 304 |
| Square root (decimal) | 17.435596 |
| Simplified radical | 4√19 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 304
304 = 2^4 × 19. This is what determines the simplified radical: for √304 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √304 = 4√19.
Estimating √304 by hand
√304 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 304 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.441176 |
| Step 2 | 17.435597 |
| Step 3 | 17.435596 |
After 3 steps the estimate is 17.435596, matching √304 ≈ 17.435596.
Nearby square roots
Frequently asked questions
Is 304 a perfect square?
No, 304 is not a perfect square, so its square root is irrational and approximately 17.435596.
What is the square root of 304 in simplest radical form?
√304 = 4√19 in simplest radical form.