Square Root Calculator › Square root of 135
Square Root of 135
√135 ≈ 11.61895
135 is not a perfect square, so √135 is an irrational number that is approximately 11.61895. In simplified radical form, √135 = 3√15.
√135 lies between √121 = 11 and √144 = 12.
| Number | 135 |
| Square root (decimal) | 11.61895 |
| Simplified radical | 3√15 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 135
135 = 3^3 × 5. This is what determines the simplified radical: for √135 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √135 = 3√15.
Estimating √135 by hand
√135 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 135 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.636364 |
| Step 2 | 11.618963 |
| Step 3 | 11.61895 |
After 3 steps the estimate is 11.61895, matching √135 ≈ 11.61895.
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Frequently asked questions
Is 135 a perfect square?
No, 135 is not a perfect square, so its square root is irrational and approximately 11.61895.
What is the square root of 135 in simplest radical form?
√135 = 3√15 in simplest radical form.