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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. 768

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. 
 
768

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student

768 = 2×2×2×2×2×2×2×2×3
= (2×2)×(2×2)×(2×2)×(2×2)×3
Here, 3 cannot be paired.
∴ We will multiply 768 by 3 to get perfect square.New number = 768×3 = 2304

2304 = 2×2×2×2×2×2×2×2×3×3
⇒2304 = (2×2)×(2×2)×(2×2)×(2×2)×(3×3)
2304 = 22×22×22×22×32
⇒ 2304 = (2×2×2×2×3)2
⇒ √2304 = 2×2×2×2×3 = 48
Thanks

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