Cube Root of 216: Methods and Sample Questions

The cube root of 216 is a value that, when multiplied by itself three times, gives the original value. 

• It is written as ³√216. 
• Due to the volume of a cube being equal to its sides cubed, the cube root of a number gives the value of the side of the geometrical shape, i.e. a cube.
• Cube root value of 216 is 6.

Read More: NCERT Solutions for Class 8 Mathematics Cube and Cube Roots

Key Terms: Cube Root of 216, Multiplication, Cube Root, Natural Number, Prime Factorization, Cube, Exponential Form

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What is a Cube Root of 216?

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It is already known that volume = side³ to find the volume of a cube but to find the side of a cube, one must take the cube root of the volume.

• Cubing is similar to squaring in that the number is multiplied three times rather than two times as in squaring. 
• The exponent for cubes is 3, which is also represented by the superscript³
• As a result, one can define the cube root as the inverse operation of cubing a number. 
• It is the "radical" symbol (used for square roots) with a little three to represent cube roots. 
• It is represented as ³√.
• For Example, 

2³ = 8, or the cube root of 8 is 2

3³ = 27, or the cube root of 27 is 3

4³ = 64, or the cube root of 64 is 4

Read More: Cube Root 1 to 30

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How to find the Cube Root of 216?

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One can find the factors of a given number by using the prime factorization method. When we take the cube root of the same number, one can see that the identical factors in the group of three can be represented as cubes. Now, the cube root effectively cancels the cubed number contained within it.

Let us take it one step at a time.

Step 1: Determine the 216 prime factors.

216 = 2 × 2 × 2 × 3 × 3 × 3

Step 2: It is obvious that 216 is a perfect cube. As a result, group the 216 factors into pairs of three and write them in the form of cubes.

216 = (2 × 2 × 2) × (3 × 3 × 3)

216 = 2³ × 3³

Using the exponentiation law, we get;

[ a^mb^m = (ab)^m] 216 = 6³

Step 3: Now use cube root on both sides to extract the factor as a single term in cubes.

³√216 = ³√(6³)

As a result, the cube root cancels out the cube of 6.

Hence, ³√216 = 6

Read More: Cube Root of 729

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Cube Root using Division Method

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Follow the steps below to find the cube root using the division method.

• Make a pair of three-digit numbers going from back to front.
• Locate the number whose cube root is less than or equal to the given number.
• Subtract the result from the given number and record the result in the second number.
• Find the multiplication factor for the next step in the long division method by multiplying the first number obtained. Repeat the procedure to find the cube root of a number.
• When the given number is not a perfect cube number, this method is used.

Read More: Cube Root of 64

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Is 216's Cube Root Irrational?

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No, because ³√216 = ³√(2× 2 ×2 × 3 ×3 ×3) can be expressed in the form p/q, i.e. 6/1. As a result, the cube root of 216 has an integer value (rational).

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Perfect Cubes Table

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Finding the cube root of perfect cubes up to three digits is simple if one memorizes the table below.

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Things to Remember

• The cube root of 216 is a value that, when multiplied by itself three times, yields the original value.
• One can find the factors of a given number by using the prime factorization method. 
• When one takes the cube root of the same number, it can be seen that the identical factors in the group of three can be represented as cubes.
• In contrast to square roots, cube roots should not be concerned with the negative values under the radical sign. 
• As a result, perfect cubes with negative values are possible.
• The dimensions of a three-dimensional object with a given value can be calculated using cube roots.
• The cube root of 216 has an integer value (rational).