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Question

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


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Solution

Step 1: Find prime factors of the given number

By the method of prime factorization, the factors of 2028 can be determined as follows,

So, 2028=2×2×3×13×13

2028=2×2¯×3×13×13¯

Here, it can be observed that the prime factors 2 and 13 form a pair, while 3 does not form a pair.

Step 2: Determine the perfect square number and its square root

Since 3 could not form a pair.

Therefore, a perfect square number can be obtained by multiplying 2028 by 3.

So, the perfect square number =2028×3=6084

Now, the square root of the above perfect square number is,

6084=2×2×3×13×13×3

6084=2×2¯×3×3¯×13×13¯

6084=2×3×13

6084=78

Hence, the smallest whole number by which 2028 should be multiplied to get a perfect square is 3 and the required perfect square number and its square root are 6084 and 78 respectively.


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