Find the cube – root of: 27 64 .

The rational number is 27 64 . The cube root of a given number is the number whose cube is the given number. If the cube root of the number x is y , then a cube of y is x . If x 3 = y , then y 3 = x . The factorisation of 27 64 is 3 27 3 9 3 3 1 and 4 64 4 16 4 4 1 Cube-root by factorisation: Split the given number into its primes. Form groups in triplets of the identical primes. Take one prime number from each triplet. Multiply all the prime numbers obtained in step 3 to get the required cube root. Now, 27 64 = 3 × 3 × 3 4 × 4 × 4 = 3 4 Hence, the cube root of the given rational number is 3 4 .

Find the cube – root of: 125 216 .

The rational number is 125 216 . The cube root of a given number is the number whose cube is the given number. If the cube root of the number x is y , then a cube of y is x . If x 3 = y , then y 3 = x . The factorisation of 125 216 is 5 125 5 25 5 5 1 and 6 216 6 36 6 6 1 Cube-root by factorisation: Split the given number into its primes. Form groups in triplets of the identical primes. Take one prime number from each triplet. Multiply all the prime numbers obtained in step 3 to get the required cube root. Now, 125 216 = 5 × 5 × 5 6 × 6 × 6 = 5 6 Hence, the cube root of the given rational number is 5 6 .

Find the cube – root of: 343 512 .

The rational number is 343 512 . The cube root of a given number is the number whose cube is the given number. If the cube root of the number x is y , then a cube of y is x . If x 3 = y , then y 3 = x . The factorisation of 343 512 is 7 343 7 49 7 7 1 and 8 512 8 64 8 8 1 Cube-root by factorisation: Split the given number into its primes. Form groups in triplets of the identical primes. Take one prime number from each triplet. Multiply all the prime numbers obtained in step 3 to get the required cube root. Now, 343 512 = 7 × 7 × 7 8 × 8 × 8 = 7 8 Hence, the cube root of the given rational number is 7 8 .