Finding Cube Root using Prime Factorisation

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Finding Cube root by Prime Factorization Let’s do this by examples Find cube root of 216 Let’s do prime factorization of 216 Thus, 216 = 2 × 2 × 2 × 3 × 3 × 3 Now, We make groups of 3 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = (2 × 3)3 = 63 Therefore, Cube root of 216 = 6 Find cube root of 729 Doing Prime factorization of 729 We see that 729 = 3 × 3 × 3 × 3 × 3 × 3 = 33 × 33 = (3 × 3)3 = 93 Therefore, Cube root of 729 = 9 Find cube root of 3375 Doing Prime factorization of 3375 We see that 3375 = 3 × 3 × 3 × 5 × 5 × 5 = 33 × 53 = (3 × 5)3 = 153 Therefore, Cube root of 3375 = 15 Find cube root of 6859 Doing Prime factorization of 6859 We see that 6859 = 19 × 19 × 19 = 193 Therefore, Cube root of 6859 = 19 Find cube root of 10648 Doing Prime factorization of 10648 We see that 10648 = 2 × 2 × 2 × 11 × 11 × 11 = 23 × 113 = (2 × 11)3 = 223 Therefore, Cube root of 10648 = 22 Find cube root of 74088 Doing Prime factorization of 10648 We see that 74088 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7 = 23 × 33 × 73 = (2 × 3 × 7)3 = 423 Therefore, Cube root of 74088 = 42