Square Root Calculator › Square root of 351
Square Root of 351
√351 ≈ 18.734994
351 is not a perfect square, so √351 is an irrational number that is approximately 18.734994. In simplified radical form, √351 = 3√39.
√351 lies between √324 = 18 and √361 = 19.
| Number | 351 |
| Square root (decimal) | 18.734994 |
| Simplified radical | 3√39 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 351
351 = 3^3 × 13. This is what determines the simplified radical: for √351 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √351 = 3√39.
Estimating √351 by hand
√351 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 351 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.75 |
| Step 2 | 18.735 |
| Step 3 | 18.734994 |
After 3 steps the estimate is 18.734994, matching √351 ≈ 18.734994.
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Frequently asked questions
Is 351 a perfect square?
No, 351 is not a perfect square, so its square root is irrational and approximately 18.734994.
What is the square root of 351 in simplest radical form?
√351 = 3√39 in simplest radical form.