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Question
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:
4761
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Solution
In problem, factorise the number into its prime factor.
4761 = 3 x 3 x 23 x 23
Grouping the factors into pairs of equal factors, we obtain:
4761 = (3 x 3) x (23 x 23)
No factors are left over. Hence, 4761 is a perfect square. The above expression is already grouped into equal factors:
4761 = (3 x 23) x (3 x 23)
= (3 x 23)2
Hence, 4761 is the square of 69, which is equal to 3 x 23.
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