Last updated on May 26th, 2025
The cube root of a number is a value that when multiplied thrice by itself results back to the original number. Imagine you have a cube (box) with a known volume. The cube root would then be useful to determine the length of one side of the box.
The cube root of 217 is a number , when you multiply it by itself three times, it gives 217. Let’s check a few steps and methods to calculate the cube root of 700.
Cube root of 217: ∛217 = 6.006
Exponential form of the cube root of 217 is 2171/3
Radical form of the cube root of 217 is ∛217
Use the following methods to find the cube root of a number:
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, 217
x = an approximate number close to the cube root of the number, 217. Let’s say x is 6. Therefore, 63 = 216.
Now, let’s apply the formula and find the cube root.
Here, a = 217 and x = 6
Now apply the formula:
∛a≅ x((x3+2a) / (2x3+a))
∛217 ≅ 6((63+2 × 217) / (2 × 63+217))
∛217 ≅ 6(( 216+434 ) / (2 x 216 + 217))
∛217 ≅ 6((650) / (649))
∛217 ≅ 6(1.001)
∛217 ≅ 6.006
While learning cube roots,it’s common for students to make mistakes, to avoid those here are some common mistakes listed below:
Find ∛217 + ∛117?
∛217 + ∛117
= 6.006 + 4.890
= 10.896.
To find the solution for ∛217 + ∛117, the value of ∛217 and ∛117 must be found and then added together. The answer is 10.899.
Solve for x if x³ = 217.
x3 = 217
Value of x = ∛217
x = 6.006.
To find the value of x, the given value of x3 is to be inverse and the cube root of 217 is to be found. Therefore, the answer will be 6.009.
The side length ‘s’ of a square is ∛217, find the area of the area of the square.
Length of a square ‘s’ = ∛217
The equation to find the area of square = a2
= ∛217 x ∛217
= 6.006 × 6.006
= 36.072.
The formula to find the area of a square is a2, which is ∛217 multiplied twice. Thus, the area of the square is 36.072.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.