Last updated on May 26th, 2025
A cube root of a number is a value, when it is multiplied by itself three times, gives the original number. Imagine you have a cube (box) with the known volume. The cube root helps us determine the length of one side of the box.
The cube root of 864 is the number which, when multiplied three times, we get a number that is equal to 864. Let’s explore some steps and methods to calculate the cube root of 864.
The cube root of 864: ∛864 = 9.524
The exponential form of the cube root of 864: 8641/3
The radical form of the cube root of 864: ∛864
To find the cube root of 864, we use the following methods:
We use the below formula to find the cube root using Halley’s Method;
∛a ≅ x((x3+2a) / (2x3+a))
In the formula;
a = given number, 864
x = an approximate number close to the cube root of the number, 864: 93= 729
Let’s apply the formula and find the Cube Root:
A = 864, for the approximate method we choose, x = 9, it is the nearest cube (93= 729).
Now apply the formula;
∛a ≅ x((x3+2a) / (2x3+a))
∛864 ≅ 9((93+2 × 864) / (2 × 93+864)) = 9.524
Hence, the approximate cube of 864 ≅ 9.524
While learning about cube roots, children making mistakes is common, so to avoid a few mistakes that are likely to happen, below are a few mistakes and how to avoid these:
Find the volume of a cube with side ∛864​.
Side(S) = ∛864​.
Volume = S3
Volume = 9.5243 = 864 units.
To find a cube’s volume, multiply the side length by itself three times. Here, 9.5453=864 units.
Solve for y if y³=864×2.
y3 =864×2 = 1728
y = ∛1728=12.
First, multiply 864×2=1728. Then, find the cube root of 1728, which means the number that, when multiplied by itself three times, equals 1728.
Simplify 864¹/³×864²/³
8641/3×8642/3 = 8641
8641=864.
When we multiply numbers with the same base, we add the exponents. So, 8641/3×8642/3=8641, which is 864.
Calculate ∛(864×864​).
∛864 = 9.524
9.524 × 9.524 = 90.70
To find this, we approximate each cube root as about 9.545. Then, we multiply 9.545 by 9.545 to get 91.