√207 =
3√23
≈ 14.387495
Square root of 207 — 14.387495 (3√23)
Irrational
The square root of 207 is about 14.387495, or exactly 3√23. It lies between 14 and 15.
- As a decimal
- ≈ 14.387495
- Simplified surd
- √207 = 3√23
- Between
- 14 < √207 < 15
- Squared
- 207² = 42849
- Cube root
- ∛207 ≈ 5.915482
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.
√207 = √(9 × 23) = 3√23
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 207?
About 14.387495, or exactly 3√23.
Q. Can the surd be simplified?
Yes: 207 = 9 × 23, so 3 comes out and it becomes 3√23.
Q. Between which integers does it fall?
Between 14 and 15.
Q. What is the cube root of 207?
About 5.915482.