√8 =
2√2
≈ 2.828427
Square root of 8 — 2.828427 (2√2)
Irrational
The square root of 8 is about 2.828427, or exactly 2√2. It lies between 2 and 3.
- As a decimal
- ≈ 2.828427
- Simplified surd
- √8 = 2√2
- Between
- 2 < √8 < 3
- Squared
- 8² = 64
- Cube root
- ∛8 = 2
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.
√8 = √(4 × 2) = 2√2
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 8?
About 2.828427, or exactly 2√2.
Q. Can the surd be simplified?
Yes: 8 = 4 × 2, so 2 comes out and it becomes 2√2.
Q. Between which integers does it fall?
Between 2 and 3.
Q. What is the cube root of 8?
2.