Question

Find the least number of four digits which is a perfect square. [3 MARKS]

Answer 1

Concept :1 Mark
Application :1 Mark
Calculation : 1 Mark

We know that the least number of 4 digits is 1000.

In order to find the least number of four digits which is a perfect square, we must first find the smallest number that must be added to 1000 to make it a perfect square. For this, we work out the process of finding the square root by long division method as given below.

$\begin{array}{cc}& 31\\ 3& \overline{10}\overline{00}\\ & 9\\ 61& 100\\ & 61\\ & 39\end{array}$

$\begin{array}{cc}& 32\\ 3& \overline{10}\overline{00}\\ & 9\\ 62& 100\\ & 124\end{array}$

It follows from this that 1000 is (124 - 100) = 24 less than $(32{)}^2$. Thus, if we add 24 to 1000, it becomes a perfect square.

Hence, the smallest number of four digits which is a perfect square is (1000 + 24) = 1024.