Cube Root Formula
The cube root formula helps in the calculation of the cube root of any given number. The cube root of a number is defined as the number which when multiplied three times gives the original number. The cube root of a number is expressed in radical form using the symbol ∛. Let us understand the cube root formula using solved examples.
What is Cube Root Formula?
Cube root of a number can be calculated by first finding out the prime factorization of the given number and then later applying the cube root formula. Suppose, x is any number such that, x = y × y × y. The formula to calculate the cube root is given as:
Cube root of x = \(\sqrt[3]{x}\) = y
where,
y is the cube root of any number x.
This also means that the number x would a perfect cube if y has an integer value.
Let's take a quick look at a couple of examples to understand the cube root formula, better.
Solved Examples Using Cube Root Formula

Example 1: Calculate the cube root of 343.
Solution:
To find: Cube root of 343
Using the cube root formula,
Cube root of 343 = \(\sqrt[3]{343} = \sqrt[3]{7 \times 7 \times 7 }\)
= 7
Answer: The cube root of 343 = 7.

Example 2: Check whether 512 is a perfect cube or not.
Solution:
To find: Whether 512 is the perfect cube or not.
Using the cube root formula,
Cube root of 512 = \(\sqrt[3]{512} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 } = \sqrt[3]{8 \times 8 \times 8} \)
= 8, which is an integer. Therefore, 512 is a perfect cube.
Answer: 512 is a perfect cube.