√117 =
3√13
≈ 10.816654
Square root of 117 — 10.816654 (3√13)
Irrational
The square root of 117 is about 10.816654, or exactly 3√13. It lies between 10 and 11.
- As a decimal
- ≈ 10.816654
- Simplified surd
- √117 = 3√13
- Between
- 10 < √117 < 11
- Squared
- 117² = 13689
- Cube root
- ∛117 ≈ 4.890973
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.
√117 = √(9 × 13) = 3√13
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 117?
About 10.816654, or exactly 3√13.
Q. Can the surd be simplified?
Yes: 117 = 9 × 13, so 3 comes out and it becomes 3√13.
Q. Between which integers does it fall?
Between 10 and 11.
Q. What is the cube root of 117?
About 4.890973.