Square Root Calculator › Square root of 12
Square Root of 12
√12 ≈ 3.464102
12 is not a perfect square, so √12 is an irrational number that is approximately 3.464102. In simplified radical form, √12 = 2√3.
√12 lies between √9 = 3 and √16 = 4.
| Number | 12 |
| Square root (decimal) | 3.464102 |
| Simplified radical | 2√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 12
12 = 2^2 × 3. This is what determines the simplified radical: for √12 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √12 = 2√3.
Estimating √12 by hand
√12 falls between √9 = 3 and √16 = 4, so it starts at 3.something. The Babylonian method refines that guess by averaging it with 12 ÷ the guess:
| Step | Estimate |
| Start | 3 |
| Step 1 | 3.5 |
| Step 2 | 3.464286 |
| Step 3 | 3.464102 |
After 3 steps the estimate is 3.464102, matching √12 ≈ 3.464102.
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Frequently asked questions
Is 12 a perfect square?
No, 12 is not a perfect square, so its square root is irrational and approximately 3.464102.
What is the square root of 12 in simplest radical form?
√12 = 2√3 in simplest radical form.