Square Root Calculator › Square root of 356
Square Root of 356
√356 ≈ 18.867962
356 is not a perfect square, so √356 is an irrational number that is approximately 18.867962. In simplified radical form, √356 = 2√89.
√356 lies between √324 = 18 and √361 = 19.
| Number | 356 |
| Square root (decimal) | 18.867962 |
| Simplified radical | 2√89 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 356
356 = 2^2 × 89. This is what determines the simplified radical: for √356 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √356 = 2√89.
Estimating √356 by hand
√356 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 356 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.888889 |
| Step 2 | 18.867974 |
| Step 3 | 18.867962 |
After 3 steps the estimate is 18.867962, matching √356 ≈ 18.867962.
Nearby square roots
Frequently asked questions
Is 356 a perfect square?
No, 356 is not a perfect square, so its square root is irrational and approximately 18.867962.
What is the square root of 356 in simplest radical form?
√356 = 2√89 in simplest radical form.