Question

How do you find the cube root of 64?

Answer 1

Hint:
First we need to find the factors of the given number to calculate the cube root. Factors are the number which completely divide the number without leaving any remainder behind. the cube root of a $\sqrt[3]{{64}}$ can be calculated by prime factorization of the number. Prime factorization is defined as expressing a number as a product of prime numbers. The numbers which are divisible by 1 and itself, i.e., it should only have two factors called prime numbers.

Complete step by step solution:
Given the number to simplify is $\sqrt[3]{{64}}$
First we will find the cube root of $64$ by finding its prime factors. Cube root of a number can be simplified by prime factorization of the number.
Prime factorization involves expressing a number as a product of prime numbers.
The prime factor of $64$
$
  2|64 \\
  2|32 \\
  2|16 \\
  2|8 \\
  2|4 \\
  2 \\
 $
Hence the factor of $\left( {64} \right) = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
Now we will pair the similar factors in a group of two,
Therefore,
$
   \Rightarrow \sqrt[3]{{64}} = \sqrt[3]{{{2^6}}} \\
   \Rightarrow \sqrt[3]{{64}} = {2^{\dfrac{6}{3}}} \\
 $
After forming a pair of the similar factors, we will take a pair out of the cube root and thus, continue this process to simplify and attain the answer.
$ \Rightarrow \sqrt[3]{{64}} = {2^2} = 4$

Hence, we get the cube root of $64$ is $4$

Note:
Cube root of any number is calculated by prime factorization of the number. After prime factorization which involves expressing a number as a product of prime numbers (numbers which are divisible by and itself), we need to pair the similar factors in a group of two. Another way to simplify the cube root of any number is using the long division method, which is quite complex, and thus, the chances of getting any error is high.