Question

Find the smallest number by which the following numbers must be multiplied ,so that the product are a perfect cube: (a) 100 (b) 132 (c) 500 (d) 1323 (e) 18432​

Answer 1

Answer:

The smallest number is 7.

Solution:

To find the ‘smallest number’ by which 1323 will be multiplied, we need to factorize 1323 as under:

1323=3 \times 4411323=3×441

1323=3 \times 3 \times 1471323=3×3×147

1323=3 \times 3 \times 3 \times 491323=3×3×3×49

1323=3 \times 3 \times 3 \times 7 \times 71323=3×3×3×7×7

The above can be written as 1323=3^{3} \times 7^{2}.1323=3

3

×7

2

.

Now, 7 is not in triplet. If 7 is in triplet, then derived number will be perfect cube.

Hence, 1323 must be ‘multiplied by 7’ to get a ‘perfect cube’ as shown below:

1323=3^{3} \times 7^{3}=21 \times 21 \times 21=92611323=3

3

×7

3

=21×21×21=9261 .