Question

Find the smallest number by which 1728 must be multiplied to make a perfect ​

Answer 1

To find. the smallest number by which 1728 must be multiplied to make it a perfect square

Solution.

Here, 1728 = 2 × 864

= 2 × 2 × 432

= 2 × 2 × 2 × 216

= 2 × 2 × 2 × 2 × 108

= 2 × 2 × 2 × 2 × 2 × 54

= 2 × 2 × 2 × 2 × 2 × 2 × 27

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 9

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

We see that, 3 is the only unpaired number in the prime factorization of 1728.

Thus we have to multiply 1728 by 3 to make it a perfect square.

Here, (2 × 2 × 2 × 3 × 3)²

= 72²

= 5184, a perfect square of 72.

Answer. 3 is the smallest number by which 1728 must be multiplied to make it a perfect square.

Answer 2

Answer:

3

Step-by-step explanation:

1728

=1728

=2×864

=2×2×432

=2×2×2×216

=2×2×2×2×108

=2×2×2×2×2×54

=2×2×2×2×2×2×27

=2×2×2×2×2×2×3×9

=2×2×2×2×2×2×3×3×3

=2×2×2×2×2×2×3×3×3

=(2×2) (2×2) (2×2) (3×3) (3)

here is no pair for 3

therefore we should multiply by 3.

I hope my answer is correct and it is useful to you.

Mark me as brainlist