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Step-by-step explanation:
Solution for (i) 1728
Just list down the factors of 1728
If you take the root of it,
This factor of 3 is limiting 1728 from becoming a perfect square.
Hence we need to divide 1728 by 3 to obtain a perfect square.
The perfect square number would be 2³×3 = 24
Similarly, you can proceed for other options too.
Small tip: You need to understand that a number would be perfect square if and only if all the prime factors which compose the number have even powers. In the case of 1728, we have two factors, 2 and 3. 2 has the power 6 and 3 has the power 3. Since, 2 has even power we are going to ignore it and focus on 3 which has odd power (3).
What is the minimum we can do to reduce the power of prime factor 3 to an even number. The closest even power is 2. Hence, we divide the whole number by 3¹.