Table of Contents

**Cube Root Formula**

**Introduction to 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.

**Cube Root Formula**

The 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 = ∛x = ∛(y × y × y) = y

where,

y is the cube root of any number x.

This also means that the number x would be a perfect cube if y has an integer value.

**Applications of Cube Root Formula**

Given below are a few major applications of cube root formula,

- solve cubic equations.
- find the dimensions of a cube if the volume is given.
- provide a more precise dimension of the apartment.

**Cube Root Formula for Negative Numbers**

To find the cube root of any number, the prime factorization method is the best way out.

In the case of negative numbers as well, perform the prime factorization of the given number.

Divide the factors obtained into three groups, each of which should contain the same number of each factor.

Multiply the factors in any one group to get the cube root.

It’s just that the product of three negative values gives us a negative result. which is represented by the negative sign with the cube root of a negative number.

Let’s take a quick look at a couple of examples to understand the cube root formula, better.

**Solved Examples on 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 = ∛343 = ∛(7×7×7) = 7

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 = ∛512 = ∛(2×2×2×2×2×2×2×2×2) = ∛(8×8×8) = 8,

which is an integer. Therefore, 512 is a perfect cube.

**Example 3:** Calculate Ron’s age if his age is the cube root of his grandmother’s age, while her present age is 64 years.

Solution:

To find: Ron’s age if his age is the cube root of his grandmother’s age

His grandmother’s age = 64 years.

Using the cube root formula,

Ron’s age= cube root of 64 = ∛64 years = 4 years.

**Frequently Asked Questions on Cube Root Formula**

1: What Is the Cube Root Formula in Algebra?

Answer: In math, the cube root formula is used to represent any number in the form of its cube root, such as for any number x, its cube root will be ∛ x = x1/3.

For example, the cube root of 125 is 5 because 5 × 5 × 5 = 125.

2: What Is the Cube Root Formula for Negative Numbers?

Answer: Yes, it is possible to find the cube root of negative numbers.

For example, -64 = (-4) × (-4) × (-4). We can write -64 as the product of 3 negative 4’s.

Thus, ∛-64 = -4 because the product of three negative values gives us a negative result.

3: How to Use Cube Root Formula?

Answer: In order to use the cube root formula

Step 1: Determine the prime factors of the number, say x using the prime factorization method.

Step 2: Make three groups of factors so obtained, containing the same number of each factor.

Step 3: Write that in the form of ∛ x = ∛ (y×y×y), where y corresponds to the cube root of x.

4: How to Write Cube Root Formula in Words?

Answer: The cube root of any number is the number raised to the power of 1/3.

5: What is the difference between the square root and cube root?

Answer: A cube root is a number, which when cubed gives the radicand, whereas the square root is a number which when squared gives the radicand. Also, the cube root of a negative number can be negative whereas the square root of a negative number cannot be negative.

6: Can we find the cube root for negative numbers?

Answer: Yes, we can find the cube root of a negative number. For example, the cube root of -64 is -4.

7: How to find the cube root of a number?

Answer: The cube root of a number can be found using the prime factorization method or the long division method.

8: What is the cube root of 512?

Answer: The cube root of 512 is 8 because 512 is a perfect cube. When 8 is multiplied thrice, we get 512.