√208 =
4√13
≈ 14.422205
Square root of 208 — 14.422205 (4√13)
Irrational
The square root of 208 is about 14.422205, or exactly 4√13. It lies between 14 and 15.
- As a decimal
- ≈ 14.422205
- Simplified surd
- √208 = 4√13
- Between
- 14 < √208 < 15
- Squared
- 208² = 43264
- Cube root
- ∛208 ≈ 5.924992
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.
√208 = √(16 × 13) = 4√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 208?
About 14.422205, or exactly 4√13.
Q. Can the surd be simplified?
Yes: 208 = 16 × 13, so 4 comes out and it becomes 4√13.
Q. Between which integers does it fall?
Between 14 and 15.
Q. What is the cube root of 208?
About 5.924992.