Cube Root of 162
Cube Root Calculator
What is the cube root of 162?
Answer
∛162 =
3∛6 ≈ 5.4514
Real cube root: the only number whose cube is 162.
≈ — rounded to 4 decimal places. 162 is not the cube of a rational number, so ∛162 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 162 = 2 × (3 × 3 × 3) × 3 = 2 × 3⁴
- Take out of the root
- ∛162 = ∛(3³ × 6) = 3∛6
- Between cubes
- 5³ = 125 < 162 < 216 = 6³, so 5 < ∛162 < 6 and ∛162 ≈ 5.4514
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FAQ
What is the cube root of 162?
∛162 = 3∛6 ≈ 5.4514
How to simplify ∛162?
Factor 162 into primes: 162 = 2 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛162 = ∛(3³ × 6) = 3∛6.
Is ∛162 a rational number?
No: 162 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 ∛162 is irrational; its decimal never ends and never repeats: ∛162 ≈ 5.4514.
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