Square Root Calculator › Square root of 132
Square Root of 132
√132 ≈ 11.489125
132 is not a perfect square, so √132 is an irrational number that is approximately 11.489125. In simplified radical form, √132 = 2√33.
√132 lies between √121 = 11 and √144 = 12.
| Number | 132 |
| Square root (decimal) | 11.489125 |
| Simplified radical | 2√33 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 132
132 = 2^2 × 3 × 11. This is what determines the simplified radical: for √132 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √132 = 2√33.
Estimating √132 by hand
√132 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 132 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.5 |
| Step 2 | 11.48913 |
| Step 3 | 11.489125 |
After 3 steps the estimate is 11.489125, matching √132 ≈ 11.489125.
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Frequently asked questions
Is 132 a perfect square?
No, 132 is not a perfect square, so its square root is irrational and approximately 11.489125.
What is the square root of 132 in simplest radical form?
√132 = 2√33 in simplest radical form.