Square Root Calculator › Square root of 343
Square Root of 343
√343 ≈ 18.520259
343 is not a perfect square, so √343 is an irrational number that is approximately 18.520259. In simplified radical form, √343 = 7√7.
√343 lies between √324 = 18 and √361 = 19.
| Number | 343 |
| Square root (decimal) | 18.520259 |
| Simplified radical | 7√7 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 343
343 = 7^3. This is what determines the simplified radical: for √343 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √343 = 7√7.
Estimating √343 by hand
√343 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 343 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.527778 |
| Step 2 | 18.520261 |
| Step 3 | 18.520259 |
After 3 steps the estimate is 18.520259, matching √343 ≈ 18.520259.
Nearby square roots
Frequently asked questions
Is 343 a perfect square?
No, 343 is not a perfect square, so its square root is irrational and approximately 18.520259.
What is the square root of 343 in simplest radical form?
√343 = 7√7 in simplest radical form.