Cube root of 512

The cube root of 512 is 8. The cube root of 512 is expressed as ∛512 in radical form, where the ∛  sign is called the radical sign. In exponential form, it is written as (512)^⅓
 

We can find the cube root of 512, mainly through two methods: 

1. Prime Factorization method.
2. Subtraction method.
    

Finding a cube root of 512 through the Prime Factorization method involves determining the factor of 512.

Step 1 — Find the prime factors of 512. 

So the prime factor of 512 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Step 2 — Group the factors of 512 in a group of 3.

Step 3–We have 9 digits, which makes a set of 3 triplets. 

Note: During Prime factorization, a pair of 2 digits is made in square roots, whereas in a cube a triplet is made. 
The cube root of 512 can be written as ∛512 = ∛(2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 2 × 2 × 2 = 8. Therefore, the cube root of 512 is 8.
 

The subtraction method involves subtracting successive numbers repeatedly. 

Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397……..successively till we get a zero. 

Subtracting the successive number method is based on the properties of cubes and the differences between consecutive cubes. Here, the subtraction took place in 8 steps to reach zero. Hence, the cube root of 512 is 8. 
 

• Powers: Powers are the degrees of a particular number, which can be used to represent squares/cubes of numbers.

• Perfect Cube: It is the product of a particular number when multiplied by itself.