Question

express the following in the index .
cube root of 216 . ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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