Theory:

Steps to find the square of a number using the diagonal method:
Step 1: Count the number of digits in the given number.
 
Step 2: Form a square block with the number of rows and columns equal to the number of digits in the block.
 
Step 3: On the top and right sides of the blocks, write the given number.
 
Step 4: Divide each square block by diagonals.
 
Step 5: Multiply the digits at the top of the column by the digits on the row's right side. Write the product's tens digit above the diagonal and the product's units digit below the corresponding square block's diagonal.
 
Step 6: Add the digits diagonally starting from the bottom right.
 
Step 7: Finally, write the number starting from the top-left side and ending at the bottom right side. We obtained the square of the given number.
Example:
Find the square of \(367\) using the diagonal method.
 
Solution:
 
Step 1: Given number is \(367\). There are \(3\) digits in the given number.
 
Step 2: Now, create a \(3 \times 3\) square block.
 
Step 3: Write \(367\) on the top side and right side of the square block.
 
Step 4: Divide each square block by diagonals.
 
Step 5: Place the product value, say, \(3 \times 7 = 21\), \(2\) in the upper part and \(1\) in the lower part of the square. Similarly, fill all the square blocks.
 
Step 6: Now, add the digits on the diagonal starting from the bottom right \((9)\).
 
Step 7: The arrow indicated numbers from left to right is \(134689\).
 
diagonal.png
 
Therefore, the square of the number \(367\) is \(134689\).