Question

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

Answer 1

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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 1323=3³ × 7².

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=3³× 7³=21 × 21 × 21=9261.

Answer 2

Step-by-step explanation:

use the method of substitution