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    Cube Root of 1701

    Cube Root Calculator
    Cube root of

    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

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    https://calculat.io/en/number/cube-root/1701Copy
    <a href="https://calculat.io/en/number/cube-root/1701">Cube Root of 1701 (∛1701): Exact Value and Decimal</a>Copy
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    Cube Root of 1701 (∛1701): Exact Value and Decimal. ∛1,701 = 3∛63 ≈ 11.9372. 1,701 = 3³ × 63, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1701/generated.jpgCopy

    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
    Recalculate with different values ↑

    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