Question

Find the smallest number by which 12748 be multiplied so that the product is a perfect square

Answer 1

Given:

Product of 12748 and the smallest number results in a "perfect square".

To find:

"The smallest number"

"Square root" of the resulting number

Answer:    

12748 = 2 × 2 × 3187

√12748 = √2 × √2 × √3187 = 2√3187

Since 3187 is a "prime number". Hence 12748 should be multiplied with 3187 to get the perfect square

That means,

12748 × 3187 = 2 × 2 × 3187 × 3187 = 40627876

√40627876 = 6374

Answer 2

Answer:

Prime factoriZation of 12748=2×2×3187

On grouping the factors in pairs, we notice that one 3187 is left out. Hence, we

should multiply 12748 with 3187, so that prime factor 3187 gets grouped in pairs.

Hence, 12748 should be multiplied by 3187 to make it a perfect square.

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