Cube Root of 1715

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What is the cube root of 1,715?

Answer

∛1,715 =
7∛5 ≈ 11.9698

Real cube root: the only number whose cube is 1,715.

≈ — rounded to 4 decimal places. 1,715 is not the cube of a rational number, so ∛1,715 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,715 = 5 × (7 × 7 × 7) = 5 × 7³
Take out of the root
∛1,715 = ∛(7³ × 5) = 7∛5
Between cubes
11³ = 1,331 < 1,715 < 1,728 = 12³, so 11 < ∛1,715 < 12 and ∛1,715 ≈ 11.9698

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,5368∛3 ≈ 11.538
1,700≈ 11.9348
1,7013∛63 ≈ 11.9372
1,7157∛5 ≈ 11.9698
1,725≈ 11.9931
1,726≈ 11.9954
1,72812

FAQ

What is the cube root of 1,715?

∛1,715 = 7∛5 ≈ 11.9698

How to simplify ∛1,715?

Factor 1,715 into primes: 1,715 = 5 × 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: ∛1,715 = ∛(7³ × 5) = 7∛5.

Is ∛1,715 a rational number?

No: 1,715 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 ∛1,715 is irrational; its decimal never ends and never repeats: ∛1,715 ≈ 11.9698.

See Also