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Which smaller number should be used to divide $3650$ to get a perfect square?

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142

152

146

154

answer is C.

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Detailed Solution

Given number is 3650.
Writing the prime factors of 3650.

3650 = 2 \times 5 \times 5 \times 73

The prime factors

2

and

73

does not have a pair.
So to get a perfect square, we have to divide

3650

2 \times 73 = 146

3650 \div 146 = 25

[perfect square of 5]
Thus we need to divide

3650

146

to get a perfect square.
Therefore, option (3) is correct.

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