Question

Find the smallest number by which 1323 must be multipled so that product is a perfect square?​

Answer 1

Step-by-step explanation:

1323 is divisible by 9 as sum of digits is divisible by 9 So, 1323/9 = 147

Now, 147 is divisible by 3 as sum of digits is divisible by 3. So, 147/3 = 49

so square root of 49 is 7

Answer 2

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*441

1323=3*3*147

1323=3*3*3*49

1323=3*3*3*7*7

The above can be written as : 3^3*7^3

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*7^3

= 21 *21 * 21

= 9216

.