Question

Anitha said 2744 is a perfect cube. Do you agree with Anitha?Give reasons.

Answer 1

Yes I agree with Anitha. 2744=14×14×14 so it's a cube of 14 and is thus a perfect cube as its factors are perfectly grouped without any factors being left out.

Hope it helps....
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Answer 2

Given:

Anita said the number 2744 is a perfect cube.

To Find:

Is the statement given by Anita is correct?

Solution:

The given problem can be solved using the concepts of prime factorization.

1. Factorize the number 2744 as the product of prime numbers,

=> 2744 = 2 x 1372,

=> 2744 = 2 x 2 x 686,

=> 2744 = 2 x 2 x 2 x 343,

=> 2744 = 2 x 2 x 2 x 7 x 49,

=> 2744 = 2 x 2 x 2 x 7 x 7 x 7.

=> 2744 = 2³ x 7³.

2. The cube root of 2³ x 7³ is 2 x 7 = 14.

3. Hence, the number 2744 is a perfect cube.

Therefore, the value of the cube root of 2744 is 14. The statement given by Anitha is correct.