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Question
Show that each of the following numbers is a perfect square. Also, find the numer whose square is the given number in each case:
2025
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Solution
In problem, factorise the number into its prime factor.
2025 = 3 x 3 x 3 x 3 x 5 x 5
Grouping the factors into pairs of equal factors, we obtain:
2025 = (3 x 3) x (3 x 3) x (5 x 5)
No factors are left over. Hence, 2025 is a perfect square. Moreover, by grouping 2025 into equal factors:
2025 = (3 x 3 x 5) x (3 x 3 x 5)
= (3 x 3 x 5)2
Hence, 2025 is the square of 45, which is equal to 3 x 3 x 5.
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