Find the cube root of 3375 5832

The given number is 3375 5832 . Now, 3375 5832 3 = 3375 3 5832 3 By Prime factorisation, we have 5 3375 5 675 5 135 3 27 3 9 3 3 1 2 5832 2 2916 2 1458 3 729 3 243 3 81 3 27 3 9 3 Expressing 3375 and 5832 as prime factors, we have 3375 = 5 × 5 × 5 × 3 × 3 × 3 = 15 5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 2 × 3 × 3 = 18 Thus, 3375 5832 3 = 3375 3 5832 3 = 5 × 5 × 5 × 3 × 3 × 3 3 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 3 = 15 18 = 5 6 Hence, the cube root of 3375 5832 is 5 6 .

Find the cube root of - 2744 3375

The given number is - 2744 3375 . Now, - 2744 3375 3 = - 2744 3 3375 3 By Prime factorisation, we have 5 3375 5 675 5 135 3 27 3 9 3 3 1 2 2744 2 1372 2 686 7 343 7 49 7 7 1 Expressing 2744 and 3375 as prime factors, we have 3375 = 5 × 5 × 5 × 3 × 3 × 3 = 15 2744 = 2 × 2 × 2 × 7 × 7 × 7 = 14 Thus, - 2744 3375 3 = - 2744 3 3375 3 = - 2 × 2 × 2 × 7 × 7 × 7 3 5 × 5 × 5 × 3 × 3 × 3 3 = - 14 15 Hence, the cube root of - 2744 3375 is - 14 15 .

Find the cube root of 1728 343

We need to find the cube root of 1728 343 We can find the cube root using the method of prime factorisation. 2 1728 2 864 2 432 2 216 2 108 2 54 3 27 3 9 3 3 1 7 343 7 49 7 7 1 So, 1728 343 3 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 7 × 7 × 7 3 = 12 7 Hence, the cube root of 1728 343 = 12 7

Find the cube root of 343000 531441

We need to find the cube root of 343000 531441 We can find the cube root using the method of prime factorisation. 3 531441 3 177147 3 59049 3 19683 3 6561 3 2187 3 729 3 243 3 81 3 27 3 9 3 3 1 7 343 7 49 7 7 1 So, 343000 531441 3 = 7 × 7 × 7 × 10 × 10 × 10 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 3 = 70 81 Hence, the cube root of 343000 531441 = 70 81

Find the cube root of 864 1372

We need to find the cube root of 864 1372 We can find the cube root using the method of prime factorisation. 2 864 2 432 2 216 2 108 2 54 3 27 3 9 3 3 1 2 1372 2 686 7 343 7 49 7 7 1 So, 864 1372 3 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 2 × 2 × 7 × 7 × 7 3 = 6 7 Hence, the cube root of 864 1372 = 6 7

Find the cube root of 8575 1600

We need to find the cube root of 8575 1600 We can find the cube root using the method of prime factorisation. 5 8575 5 1715 7 343 7 49 7 7 1 2 1600 2 800 2 400 2 200 2 100 2 50 5 25 5 5 1 So, 8575 1600 3 = 7 × 7 × 7 × 5 × 5 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 3 = 7 4 Hence, the cube root of 8575 1600 = 7 4

Find the cube root of 0 . 064 3 . 375

We need to find the cube root of 0 . 064 3 . 375 0 . 064 3 . 375 = 64 1000 3375 1000 = 64 3375 We can find the cube root using the method of prime factorisation. 2 64 2 32 2 16 2 8 2 4 2 5 3375 5 675 5 135 3 27 3 9 3 3 1 So, 64 3375 3 = 2 × 2 × 2 × 2 × 2 × 2 5 × 5 × 5 × 3 × 3 × 3 3 = 4 15 Hence, the cube root of 0 . 064 3 . 375 = 4 15

Show that: 8 3 × 729 3 = 8 × 729 3

We need to show that, 8 3 × 729 3 = 8 × 729 3 L.H.S We need to find the value of 8 3 × 729 3 We can find the cube root of 8 and 729 by prime factorisation method. 2 8 2 4 2 2 1 3 7 2 9 3 2 4 3 3 8 1 3 2 7 3 9 3 3 1 8 3 = 2 × 2 × 2 3 = 2 and 729 3 = 3 × 3 × 3 × 3 × 3 × 3 3 = 9 8 3 × 729 3 = 18 RHS: 8 × 729 3 = 5832 3 2 5832 2 2916 2 1458 3 729 3 243 3 81 3 27 3 9 3 3 1 8 × 729 3 = 5832 3 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 3 = 2 × 3 × 3 = 18 Since LHS = RHS, hence proved.