Cube Root of 625
Cube Root Calculator
What is the cube root of 625?
Answer
∛625 =
5∛5 ≈ 8.5499
Real cube root: the only number whose cube is 625.
≈ — rounded to 4 decimal places. 625 is not the cube of a rational number, so ∛625 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 625 = (5 × 5 × 5) × 5 = 5⁴
- Take out of the root
- ∛625 = ∛(5³ × 5) = 5∛5
- Between cubes
- 8³ = 512 < 625 < 729 = 9³, so 8 < ∛625 < 9 and ∛625 ≈ 8.5499
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See Also
- 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 625?
∛625 = 5∛5 ≈ 8.5499
How to simplify ∛625?
Factor 625 into primes: 625 = 5 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛625 = ∛(5³ × 5) = 5∛5.
Is ∛625 a rational number?
No: 625 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 ∛625 is irrational; its decimal never ends and never repeats: ∛625 ≈ 8.5499.
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