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What is the cube root of 1,701?

Answer

∛1,701 =
3∛63 ≈ 11.9372

Real cube root: the only number whose cube is 1,701.

≈ — rounded to 4 decimal places. 1,701 is not the cube of a rational number, so ∛1,701 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,701 = (3 × 3 × 3) × 3 × 3 × 7 = 3⁵ × 7
Take out of the root
∛1,701 = ∛(3³ × 63) = 3∛63
Between cubes
11³ = 1,331 < 1,701 < 1,728 = 12³, so 11 < ∛1,701 < 12 and ∛1,701 ≈ 11.9372

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,521≈ 11.5003
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

FAQ

What is the cube root of 1,701?

∛1,701 = 3∛63 ≈ 11.9372

How to simplify ∛1,701?

Factor 1,701 into primes: 1,701 = 3 × 3 × 3 × 3 × 3 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,701 = ∛(3³ × 63) = 3∛63.

Is ∛1,701 a rational number?

No: 1,701 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 ∛1,701 is irrational; its decimal never ends and never repeats: ∛1,701 ≈ 11.9372.

See Also