Find the smallest number by which 12748 be multiplied so that the product is a perfect square
Answers
Answered by
25
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
Answered by
10
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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