Square Root Calculator › Square root of 352
Square Root of 352
√352 ≈ 18.761663
352 is not a perfect square, so √352 is an irrational number that is approximately 18.761663. In simplified radical form, √352 = 4√22.
√352 lies between √324 = 18 and √361 = 19.
| Number | 352 |
| Square root (decimal) | 18.761663 |
| Simplified radical | 4√22 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 352
352 = 2^5 × 11. This is what determines the simplified radical: for √352 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √352 = 4√22.
Estimating √352 by hand
√352 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 352 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.777778 |
| Step 2 | 18.76167 |
| Step 3 | 18.761663 |
After 3 steps the estimate is 18.761663, matching √352 ≈ 18.761663.
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Frequently asked questions
Is 352 a perfect square?
No, 352 is not a perfect square, so its square root is irrational and approximately 18.761663.
What is the square root of 352 in simplest radical form?
√352 = 4√22 in simplest radical form.