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Question
Show that 500 is not a perfect square.
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Solution
Factors of 500 are 2 × 2 × 5 × 5 × 5
Now, group the factors into pairs, we get
500 = (2 × 2) × (5 × 5 × 5)
= 22 × 53
So, the prime factors 2 and 5 do not occur in pairs.
Hence, 500 is not a perfect square.
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