Square Root Calculator › Square root of 332
Square Root of 332
√332 ≈ 18.220867
332 is not a perfect square, so √332 is an irrational number that is approximately 18.220867. In simplified radical form, √332 = 2√83.
√332 lies between √324 = 18 and √361 = 19.
| Number | 332 |
| Square root (decimal) | 18.220867 |
| Simplified radical | 2√83 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 332
332 = 2^2 × 83. This is what determines the simplified radical: for √332 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √332 = 2√83.
Estimating √332 by hand
√332 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 332 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.222222 |
| Step 2 | 18.220867 |
| Step 3 | 18.220867 |
After 3 steps the estimate is 18.220867, matching √332 ≈ 18.220867.
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Frequently asked questions
Is 332 a perfect square?
No, 332 is not a perfect square, so its square root is irrational and approximately 18.220867.
What is the square root of 332 in simplest radical form?
√332 = 2√83 in simplest radical form.