Square Root Calculator › Square root of 32
Square Root of 32
√32 ≈ 5.656854
32 is not a perfect square, so √32 is an irrational number that is approximately 5.656854. In simplified radical form, √32 = 4√2.
√32 lies between √25 = 5 and √36 = 6.
| Number | 32 |
| Square root (decimal) | 5.656854 |
| Simplified radical | 4√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 32
32 = 2^5. This is what determines the simplified radical: for √32 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √32 = 4√2.
Estimating √32 by hand
√32 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 32 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.7 |
| Step 2 | 5.657018 |
| Step 3 | 5.656854 |
After 3 steps the estimate is 5.656854, matching √32 ≈ 5.656854.
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Frequently asked questions
Is 32 a perfect square?
No, 32 is not a perfect square, so its square root is irrational and approximately 5.656854.
What is the square root of 32 in simplest radical form?
√32 = 4√2 in simplest radical form.