√126 =
3√14
≈ 11.224972
Square root of 126 — 11.224972 (3√14)
Irrational
The square root of 126 is about 11.224972, or exactly 3√14. It lies between 11 and 12.
- As a decimal
- ≈ 11.224972
- Simplified surd
- √126 = 3√14
- Between
- 11 < √126 < 12
- Squared
- 126² = 15876
- Cube root
- ∛126 ≈ 5.013298
How the surd is simplified
Pull out the largest square factor. Since 50 = 25 × 2, the root of 25 comes out as 5 and the 2 stays behind: 5√2.
√126 = √(9 × 14) = 3√14
Nearby numbers
From 1 to 200
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How to read this
- The decimal is rounded; the surd form is the exact value.
- Pulling out a square factor simplifies the surd — √50 = 5√2.
- If the number is not a perfect square, the decimal never ends (irrational).
- Knowing which two integers it sits between is enough to estimate in your head.
Frequently asked questions
Q. What is the square root of 126?
About 11.224972, or exactly 3√14.
Q. Can the surd be simplified?
Yes: 126 = 9 × 14, so 3 comes out and it becomes 3√14.
Q. Between which integers does it fall?
Between 11 and 12.
Q. What is the cube root of 126?
About 5.013298.