√76 =
2√19
≈ 8.717798
Square root of 76 — 8.717798 (2√19)
Irrational
The square root of 76 is about 8.717798, or exactly 2√19. It lies between 8 and 9.
- As a decimal
- ≈ 8.717798
- Simplified surd
- √76 = 2√19
- Between
- 8 < √76 < 9
- Squared
- 76² = 5776
- Cube root
- ∛76 ≈ 4.235824
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.
√76 = √(4 × 19) = 2√19
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 76?
About 8.717798, or exactly 2√19.
Q. Can the surd be simplified?
Yes: 76 = 4 × 19, so 2 comes out and it becomes 2√19.
Q. Between which integers does it fall?
Between 8 and 9.
Q. What is the cube root of 76?
About 4.235824.