Square Root Calculator › Square root of 134
Square Root of 134
√134 ≈ 11.575837
134 is not a perfect square, so √134 is an irrational number that is approximately 11.575837. In simplified radical form, √134 = √134.
√134 lies between √121 = 11 and √144 = 12.
| Number | 134 |
| Square root (decimal) | 11.575837 |
| Simplified radical | √134 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 134
134 = 2 × 67. This is what determines the simplified radical: for √134 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √134 is already in simplest radical form as √134.
Estimating √134 by hand
√134 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 134 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.590909 |
| Step 2 | 11.575847 |
| Step 3 | 11.575837 |
After 3 steps the estimate is 11.575837, matching √134 ≈ 11.575837.
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Frequently asked questions
Is 134 a perfect square?
No, 134 is not a perfect square, so its square root is irrational and approximately 11.575837.
What is the square root of 134 in simplest radical form?
√134 = √134 in simplest radical form.