find the cube root by the prime factorisation on method = 512
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Let us understand it step by step.
Step 1: Find the prime factors of 512
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Step 2: Pair the factors of 512 in a group of three, such that they form cubes.
512 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
512 = 23 × 23 × 23
Using the law of exponent, we get;
512 = 29 [am.an = (a)m+n]
Or
512 = (23)^3 [(am)n = amn]
512 = 8^3
Step 3: Now, we will apply cube root on both the sides to take out the factor (in cubes) as a single term.
3√512 = 3√(83)
So, here the cube root is eliminated by the cube of 8.
Hence, 3√512 = 8
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