Cube root of 217

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 217^1/3

Radical form of the cube root of 217 is ∛217
 

Use the following methods to find the cube root of a number:

• Prime factorization
• Approximation method
• Long division 
• Subtraction method
• Halley’s method — is used when a number is not a perfect cube.
   

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
 

• Whole numbers — The whole numbers are the set of numbers that includes all the positive integers and zero. Example: 0,1,2,3………

• Square root  —A number’s square root is considered as a number that when it is multiplied by itself gives us the original number.Example: √4 is 2.

• Exponent: It is a number which shows how many times a base number should be multiplied by itself.Example: 4²=  4 x 4 = 16

• Irrational number: The number that cannot be written in the form of a fraction.Example: √2 is an irrational number.