Find the cube root of the following number: - 216 512

Given, - 216 512 We need to find, - 216 512 3 = - 1 3 × 216 512 3 Using prime factorization method, ⇒ - 216 512 3 = - 1 × 6 × 6 × 6 8 × 8 × 8 3 ⇒ - 216 512 3 = - 1 × 6 3 8 3 3 ∴ - 216 512 3 = - 6 8 = - 3 4 Hence, - 216 512 3 = - 3 4 .

Find the cube root of the following number: - 512 343

Given, - 512 343 3 ⇒ = - 1 3 × 512 343 3 Prime factorization of 512 and 343 is, ⇒ - 512 343 3 = - 1 × 8 × 8 × 8 7 × 7 × 7 3 ⇒ - 512 343 3 = - 1 × 8 3 7 3 3 ⇒ - 512 343 3 = - 8 7 Therefore, - 512 343 3 = - 8 7 .

Find the cube root of the following number: - 686 - 2662

Given, - 686 - 2662 3 = - 1 - 1 3 × 686 2662 3 = 686 2662 3 ∵ - 1 - 1 = 1 Using prime factorisation method, ∴ 686 = 2 × 7 × 7 × 7 = 2 × 7 3 ∴ 2662 = 2 × 11 × 11 × 11 = 2 × 11 3 ⇒ 686 2662 3 = 2 × 7 3 2 × 11 3 3 ⇒ 7 3 11 3 3 = 7 11 Therefore, 7 3 11 3 3 = 7 11 .

Find the cube root of the following number: - 1728 125

Given, - 1728 125 3 ⇒ - 1 3 × 1728 125 3 Using prime factorization, ⇒ 1728 3 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 3 = 2 3 × 2 3 × 3 3 3 ⇒ 125 3 = 5 × 5 × 5 3 = 5 3 3 ∴ - 1728 125 3 = - 1 × 2 3 × 2 2 × 3 3 5 3 3 = - 1 × 2 × 2 × 3 5 = - 12 5 Hence, - 1728 125 3 = - 12 5 .

Evaluate: - 192 3993 3

Given: - 192 3993 3 = - 2 × 2 × 2 × 2 × 2 × 2 × 3 ( 11 × 11 × 11 × 3 ) 3 = - 2 3 × 2 3 11 3 3 = - 2 × 2 11 = - 4 11 “Note: Answer mentioned in the book is incorrect the correct answer is: - 4 11 ”