Question

The least number of four digits which is a perfect square is
A. 1100
B. 1210
C. 1024
D. 1081

Answer 1

Hint: First we will write the smallest number of 4 digits. After this we will find the square root of this number by long division method. We will find that ${31^2} < 1000 < {32^2}$. It is clear from this that the required number is ${32^2}$.

Complete step-by-step answer:

The smallest number of four digits is 1000.
On finding the square root of this number by long division method, we get:

Therefore, it is clear that ${31^2} < 1000 < {32^2}$.
So, the least number of four digits which is a perfect square is ${32^2}$=1024.
Hence, option C is correct.

Note: This type of question is generally solved by finding the square root by long division method. You cannot solve it using the prime factorization method. If in the question it is asked to find the largest number of four digits which is a perfect square then in this case after finding the square root by long division method, you have to just subtract the remainder that comes to get the required number.