Question

Find the cube root of 216 by prime factorization method​

Answer 1

Answer:

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.

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Step-by-step explanation:

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Answer 2

Let us understand it step by step.

Let us understand it step by step.Step 1: Find the prime factors of 216

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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.

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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)

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using the law of exponent, we get;

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using the law of exponent, we get;216 = 63 [ambm = (ab)m]

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using 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.

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using 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)

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using 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.

Let us understand it step by step.Step 1: Find the prime factors of 216216 = 2 × 2 × 2 × 3 × 3 × 3Step 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 × 33Using 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