Question

Using prime factorisation, find the cube roots of: (a) 512 (b) 2197 (c) 2744​

Answer 1

Answer:

(a) 8 (b) 13 (c) 14

Step-by-step explanation:

(a) 512 = 2^9

Therefore cube root of 2^9 = 2^3 = 8

(b) 2197 = 13^3

Therefore cube root of 13^3 = 13

(c) 2744 = 2^3 * 7^3 = 14^3

Therefore cube root of 14^3 = 14

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Answer 2

By prime factorisation

a) 512 = 2×2×2×2×2×2×2×2

take out one from each triplet

2×2×2= 8

cube root of 512 is 8.

b)2197=13×13×13

cube root of 2197 is 13

c)2744=2×2×2×7×7×7

2×7=14

cube root of 2744 is 14