√68 =
2√17
≈ 8.246211
Square root of 68 — 8.246211 (2√17)
Irrational
The square root of 68 is about 8.246211, or exactly 2√17. It lies between 8 and 9.
- As a decimal
- ≈ 8.246211
- Simplified surd
- √68 = 2√17
- Between
- 8 < √68 < 9
- Squared
- 68² = 4624
- Cube root
- ∛68 ≈ 4.081655
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.
√68 = √(4 × 17) = 2√17
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 68?
About 8.246211, or exactly 2√17.
Q. Can the surd be simplified?
Yes: 68 = 4 × 17, so 2 comes out and it becomes 2√17.
Q. Between which integers does it fall?
Between 8 and 9.
Q. What is the cube root of 68?
About 4.081655.