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For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. 2028

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. 
2028

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
one year ago
Dear Student
2028 = 2×2×3×13×13
= (2×2)×(13×13)×3
Here, 3 cannot be paired.
∴ We will multiply 2028 by 3 to get perfect square. New number = 2028×3 = 6084

6084 = 2×2×3×3×13×13

⇒ 6084 = (2×2)×(3×3)×(13×13)

⇒ 6084 =22×32×132

⇒ 6084 = (2×3×13)2

⇒ √6084 = 2×3×13 = 78
Thanks

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