The cube root of 216 is a value which after getting multiplied by itself, thrice, gives the original value. It is expressed as 3√216. The cube root of a number gives the value of the side of the geometrical shape, i.e. a cube, because the volume of the cube is equal to its sides cubed. Hence, here 216 is supposed to be the volume of the cube and we need to find the value of its side, by taking its cubic root.
|Cube root of 216, 3√216 = 6|
Let, ‘n’ be the value obtained from 3√216, then as per the definition of cubes, n × n × n = n3 = 216. Since 216 is a perfect cube, we will use here the prime factorisation method, to get the cube root easily. Learn more in this article here.
How to Find Cube Root of 216
By the use of the prime factorisation method, we can find the factors of the given number. Now, when we take the cube root of the same number, the identical factors present in the group of three can be presented as cubes. Now, the cube root basically cancels the cubed number present within it.
Let us understand it step by step.
Step 1: Find the prime factors of 216
216 = 2 × 2 × 2 × 3 × 3 × 3
Step 2: Clearly, 216 is a perfect cube. Therefore, group the factors of 216 in a pair of three and write in the form of cubes.
216 = (2 × 2 × 2) × (3 × 3 × 3)
216 = 23 × 33
Using the law of exponent, we get;
216 = 63 [ambm = (ab)m]
Step 3: Now, we will apply cube root on both the sides to take out the factor as a single term, which is in cubes.
3√216 = 3√(63)
So, here the cube root is cancelled by the cube of 6.
Hence, 3√216 = 6
Video Lesson on Finding Cube Roots
Perfect Cubes Table
Finding the cube root of perfect cubes up to three-digit numbers is easy if we memorise the below-given table.
|Number (n)||Cubes (n3)|
But to find the cube root of four-digit numbers, we need to use the estimation method, which you can learn at BYJU’S.