Cube Root of 216

The cube root of a number is a value that, when multiplied by itself three times, results in the original number. For example, if we multiply a by itself three times to get b, then b is the cube of a, or a is the cube root of b. Given that 216 is a perfect cube, we will use the prime factorization method to easily find its cube root. This page will explain the cube root of 216 in detail.

Introduction

The cube root of 216 is a number that, when multiplied by itself three times, equals 216. Let’s denote this value as ‘n’, then according to the definition of cubes, n x n x n = n³ = 216.

Cube Root

A number cube root is the number that, when multiplied by itself three times, yields the number 'a' itself.

For example,2³=2 x 2 x 2=8 and 3³=3 x 3 x 3=27

Also Read: Cube Root of 3

How to find cube root of 216

Using the prime factorization method, the following steps can be used to find the cube root of any number. This method is used to find 3216 in this case.

Step 1 : Find the prime factors of the given number ,that is 216.

From the factor tree we can observe that,

Prime factorization of 216=222333

Imp : Prime factors of a number can always be determined from the factor tree of the number.

Step 2 : 216 is a perfect cube. Group three identical factors in one group.\

216=222333

216=2333

Using the law of exponent,we get

216=63

Step 3 : Now, we will apply cube root on both the sides,

3216= 363

So, the cube root is canceled by the cube of 6

Therefore, 3216=6

Perfect cube table

Simplify Algebraic Cube Root

To simplify algebraic cube roots, the following conditions must be met:

• There should be no fractional values under the radical sign.
• No ideal power factors should be under the cube root symbol.
• No exponent value should be greater than the index value when using the cube root symbol.
• If a fraction appears under the radical, the denominator should not contain any fractions.

When calculating the cube root of any integer, look for factors that appear in sets of three. For example, the cube of 27 is 3, since the factors of 27 are 3 x 3 x 3. Unlike square roots, cube roots can handle negative values under the radical sign, allowing for perfect cubes with negative values, unlike perfect squares which cannot be negative.

Use of Cubes and Cube Roots

Cubes and cube roots are widely used in various mathematical and physical operations, such as solving cubic equations and calculating the dimensions of three-dimensional objects. They are also common in everyday math computations, especially when studying exponents and determining the dimensions of a cube given its volume.

Cube Root of Negative Numbers

The prime factorization method is the most effective way to calculate the cube root of any integer, including negative numbers:

1. Prime factorize the given integer.
2. Group the factors into sets of three, with each set containing the same number of each component.
3. Multiply the components in each group to find the cube root.

For negative numbers, simply factorize the integer and follow the same steps, noting that the cube root of a negative number will also be negative. This is represented by a negative sign preceding the cube root.