Explain the diagonal method for squaring a number.

The steps of finding out the square by the diagonal method are given below.

1) Form a box (square/rectangle) and divide it into small boxes based on the number of digits.

2) Put a number above each column (from left to right) horizontally, and put a number beside each row (from top to bottom) vertically. Then draw the diagonals in the smaller boxes.

3) Multiply each digit beside the row of the box with each digit on the top of the column one by one.

4) If the product has a single-digit number or only a unit place number, then you can put ‘0’ in the upper part of the diagonal or you can leave it blank, and put the single-digit below the diagonal. If the product has a two-digit number, put the tens digit in the upper part of the diagonal and the unit digit in the lower part of the diagonal.

5) Now, start adding all the digits diagonally starting from the lowest diagonal.

6) Underline all the digits on the unit's place and carry over the other digit to the next and add the carry to the next number.

7) After completing this, write down all the underlined digits. This number will be the square of the given number.

For a better understanding, we are taking a random number that is ‘525’ for an example. 6th digit $= 2$ 5th digit $= 1 + 5 + 1 = 7$ 4th digit $= 2 + 0 + 0 + 0 + 2 + 1 = 5$ 3rd digit $= 5 + 1 + 4 + 1 + 5 = 16$ (1 carry forward) 2nd digit $= 2 + 0 = 2$ 1st digit $= 5$ Hence, the required number is 275625