Square Root Calculator › Square root of 350
Square Root of 350
√350 ≈ 18.708287
350 is not a perfect square, so √350 is an irrational number that is approximately 18.708287. In simplified radical form, √350 = 5√14.
√350 lies between √324 = 18 and √361 = 19.
| Number | 350 |
| Square root (decimal) | 18.708287 |
| Simplified radical | 5√14 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 350
350 = 2 × 5^2 × 7. This is what determines the simplified radical: for √350 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √350 = 5√14.
Estimating √350 by hand
√350 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 350 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.722222 |
| Step 2 | 18.708292 |
| Step 3 | 18.708287 |
After 3 steps the estimate is 18.708287, matching √350 ≈ 18.708287.
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Frequently asked questions
Is 350 a perfect square?
No, 350 is not a perfect square, so its square root is irrational and approximately 18.708287.
What is the square root of 350 in simplest radical form?
√350 = 5√14 in simplest radical form.