Question

Find the smallest no. by which 1323 must be multiplied so that the product is a perfect cube.

Answer 1

Answer:

The number should me multiplied by 7.To get a perfect cube.(1323*7=9261)

Step-by-step explanation:

Factories 1323

1323=3*3*3*7*7

Therefore the no 7 should be multiplied to the no so that we get a perfect cube.

As there is only two 7's.

so,the perfect cube

=1323*7

=2961

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Answer 2

Answer: The smallest number is 7

Step-by-step explanation: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