What is the cube root of 9261?

The cube root of 9261 is exactly 21, since 21³ = 9261.

How do you calculate the cube root of 9261?

You can compute the cube root using Newton's Method, an iterative algorithm. Starting from an initial estimate, refine it via x = (2·x + a/x²) / 3 until the value stabilizes. Convergence is quadratic — each iteration roughly doubles the digits of precision.

Cube Root of 9261 = 21.0000

Quick Answer

∛9261 = 21.0000

Because 21³ = 21 × 21 × 21 = 9261

Cube Root Calculator

Cube Root Simplify Cube Root Cubed (n³) Is N a Perfect Cube? Exponents (bⁿ)

Use the calculator above to find the cube root of any real number (positive, negative, or decimal). See below the step-by-step method using Newton's iteration, plus a table of common perfect cubes.

9261 Is a Perfect Cube

∛9261 = 21 because 21³ = 21 × 21 × 21 = 9261

Formula

The cube root of a number a is the value x such that:

x³ = a ⇔ ∛a = x

Every real number has exactly one real cube root. Unlike the square root, the cube root is defined for negative inputs: ∛(−a) = −∛a.

How to Calculate Cube Roots

For perfect cubes (8, 27, 64, 125, …) the cube root is an integer — just recall the cube of small integers.

For other numbers, use Newton's Method:

Start with a rough estimate (e.g. x₀ = a / 3).
Apply x_n+1 = (2x_n + a/x_n²) / 3.
Repeat 3–4 times — the value converges fast (each step roughly doubles the digits of precision).

Nearby Cube Roots

∛n	Result	Type
∛150	5.3133	irrational
∛200	5.8480	irrational
∛216	6.0000	perfect cube
∛250	6.2996	irrational
∛343	7.0000	perfect cube
∛500	7.9370	irrational
∛512	8.0000	perfect cube
∛729	9.0000	perfect cube
∛1000	10.0000	perfect cube
∛1728	12.0000	perfect cube
∛2000	12.5992	irrational
∛8000	20.0000	perfect cube

Perfect Cube Roots Table

Common perfect cubes from 1 to 1000. For the full table 1–100, see our cube root chart 1 to 1000.

n	∛n
1	1
8	2
27	3
64	4
125	5
216	6
343	7
512	8
729	9
1000	10

Inverse Operation: Cubing

Since ∛9261 = 21, the inverse operation is cubing: 21³ = 9261.

See our Cubed Calculator for more details on this and related cubed values.

Want the Simplified Radical Form?

The decimal value above is useful for measurements, but in algebra problems you often need the simplified radical form. Try our Simplify Cube Root Calculator to see ∛9261 in simplest form (e.g. 2∛3 instead of 21.0000).