Question

Find the least number of four digits that is a perfect square.

Answer 1

Step 1: Apply Rule $\mathbf{\left(}\mathbf{1}\mathbf{\right)}$ of long division method

Evaluate the square root of the least $4$-digit number i.e., $1000$.

According to Rule $\left(1\right)$, place a bar over the pair of numbers starting from the unit place or Right-hand side of the number.

$\overline{10}$$\overline{00}$

Step 2: Apply Rule $\mathbf{\left(}\mathbf{2}\mathbf{\right)}$ of long division method

According to Rule $\left(2\right)$, we then take the largest number as the divisor whose square is less than or equal to the number on the extreme left of the number and subtract.

Step 3: Apply Rule $\mathbf{\left(}\mathbf{3}\mathbf{\right)}$ of long division method

According to Rule $\left(3\right)$, we then bring down the number, which is under the bar, to the right side of the remainder and double the value of the quotient and enter it with blank space on the right side.



Step 4: Apply Rule $\mathbf{\left(}\mathbf{4}\mathbf{\right)}$ of long division method
According to Rule $\left(4\right)$, we have to select the largest digit for the unit place of the divisor such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than the dividend. Here, if we consider $1$ in the unit's place, then the required conditioned get fulfilled.

Step 5: Find the least number of four digits that is a perfect square.

Evaluate the square of $32$ as the square of $31$ is less than $4$-digits.

Hence, the least number of four digits that is a perfect square $\mathbf{=}\mathbf{}{\mathbf{\left(}\mathbf{32}\mathbf{\right)}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1024}$