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# 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?

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.

### Cube Root Formula

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 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.

## 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

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

= 8, which is an integer. Therefore, 512 is a perfect cube.

**Answer:** **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.

**Answer: Ron's age is 4 years**

## FAQs on Cube Root Formula

### What Is the Cube Root Formula in Algebra?

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 ^{3}√x = x^{1/3}. For example, the cube root of 125 is 5 because 5 × 5 × 5 = 125.

### What Is the Cube Root Formula for Negative Numbers?

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.

### How To Use Cube Root Formula?

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 3: Make three groups of factors so obtained, containing the same number of each factor.
- Step 3: Write that in the form of
^{3}√x =^{3}√(y×y×y), where y corresponds to the cube root of x.

### How To Write Cube Root Formula in Words?

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

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