Cube Root of 686
Cube Root Calculator
What is the cube root of 686?
Answer
∛686 =
7∛2 ≈ 8.8194
Real cube root: the only number whose cube is 686.
≈ — rounded to 4 decimal places. 686 is not the cube of a rational number, so ∛686 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 686 = 2 × (7 × 7 × 7) = 2 × 7³
- Take out of the root
- ∛686 = ∛(7³ × 2) = 7∛2
- Between cubes
- 8³ = 512 < 686 < 729 = 9³, so 8 < ∛686 < 9 and ∛686 ≈ 8.8194
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- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
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FAQ
What is the cube root of 686?
∛686 = 7∛2 ≈ 8.8194
How to simplify ∛686?
Factor 686 into primes: 686 = 2 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛686 = ∛(7³ × 2) = 7∛2.
Is ∛686 a rational number?
No: 686 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛686 is irrational; its decimal never ends and never repeats: ∛686 ≈ 8.8194.
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