Question

find the smallest number by which 1323 must be multiplied so that the product is a perfect cube

Answer 1

The smallest number is 7.  

Solution:

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

$1323=3 \times 441$

$1323=3 \times 3 \times 147$

$1323=3 \times 3 \times 3 \times 49$

$1323=3 \times 3 \times 3 \times 7 \times 7$

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

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:

$1323=3^{3} \times 7^{3}=21 \times 21 \times 21=9261$.

Answer 2

Answer:

please click the above attachment,

answer is 7...

hope it helps..