Find the cube root of 64 1331

The given number is 64 1331 . Now, 64 1331 3 = 64 3 1331 3 = 64 3 1331 3 By Prime factorisation, we have 2 64 2 32 2 16 2 8 2 4 2 2 1 11 1331 11 121 11 11 1 Expressing 64 and 1331 as prime factors, we have 64 = 2 × 2 × 2 × 2 × 2 × 2 1331 = 11 × 11 × 11 Thus, 64 1331 3 = 64 3 1331 3 = 2 × 2 × 2 × 2 × 2 × 2 3 11 × 11 × 11 3 = 2 × 2 11 = 4 11 Hence, the cube root of 64 1331 is 4 11 .

Find the cube root of 27 - 4096

The given number is 27 - 4096 . Now, 27 - 4096 3 = 27 3 - 4096 3 By Prime factorisation, we have 2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1 3 27 3 9 3 3 1 Expressing 27 and 4096 as prime factors, we have 27 = 3 × 3 × 3 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Thus, 27 - 4096 3 = 27 3 - 4096 3 = 3 × 3 × 3 3 - 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 3 = - 3 16 Hence, the cube root of 27 - 4096 is - 3 16 .

Find the cube root of: - 512 343 .

The given rational number is - 512 343 . We need to find the cube root of the given number. If m is any positive integer, then - m is a negative integer. Since, - m 3 = - m × - m × - m = - m 3 ∴ - m 3 3 = m 3 - 3 = - m Cube - root of - m 3 = - Cube - root of m 3 Prime factorisation of - 512 343 is 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 1 and 7 343 7 49 7 7 1 Now, - 512 343 = - 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 7 × 7 × 7 Take one prime number from each triplet and multiply all the prime numbers obtained to get the required cube root. That is, - 512 343 3 = - 2 × 2 × 2 7 = - 8 7 . Hence, the cube root of given number is - 8 7 .