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Question 89

Solve the following question:

Show that 500 is not a perfect square.


Solution

Resolving 500 into prime factors, we have
250022505125525551
500=2×2×5×5×5
Grouping the factors into pairs of equal factors, we get
500=(2×2)×(5×5)×5
Clearly, by grouping into pairs of equal factors, we are left with one factor 5, which cannot be paired.
Hence, 500 is not a perfect square.


Mathematics
NCERT Exemplar
Standard VIII

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