Question

Find the value of each of the following, using the diagonal method.
${(67)^2}$
\[
  {\text{A}}{\text{. 4489}} \\
  {\text{B}}{\text{. 4469}} \\
  {\text{C}}{\text{. 4459}} \\
  {\text{D}}{\text{. 4409}} \\
 \]

Answer 1

Hint: Square of a number is the multiplication of the number by itself. A diagonal method is one of the easy methods to find the square of a number. This method involves the squares which are divided into subparts depending upon the number of digits for which square is to be calculated, and each square is divided by a diagonal line. Then, the number is written on the top horizontally and to the left vertically of the square table whose square is being found. After this, each digit on the left side is multiplied with each digit on the top of table one by one then the product of the digits are written in the sub box where the unit digit is written above the diagonal and tens place digit below the diagonal. Now starting from the lowest diagonal, digits are added with their consequent digits till the uppermost diagonal.

Complete step by step answer:
The given number whose square is to be found is written in the square table, and each digit are multiplied

Now, starting from the lowermost side of the right-hand for the ones place digit and start moving upwards while adding each digit at the consequent place for the higher-order places digit.

At one's place, the digit is 9.
At tens place, the digit is the summation of \[2 + 4 + 2 = 8\]
At hundreds place, the digit in the unit place is the summation of \[4 + 6 + 4 = 14\], i.e., 4
At thousands place, the digit is the summation of 3 with 1 carry forwarded, i.e., $3 + 1 = 4$

Hence, \[{67^2} = 4489\]

Note: While adding the digits of the consequent diagonal the tens place digits are carried forward and are added to the next diagonal digits of the table. Another way of calculating the square of a number simply multiplies the number by itself by general multiplication rule; however, this method is a bit lengthy and has more calculations included.