# Square of three digit number

## Consider 3-digit number as abc. Follow these steps to better understand: Step 1: get  $$\mathbf{c^{2}}$$ by multiplying right side digits [c$$\times$$c] Step 2: get 2bc by criss-cross product of b and c [(b$$\times$$c)+(b$$\times$$c)=2bc] Step 3: get 2ac+ $$\mathbf{b^{2}}$$ by criss-cross product of a and c, criss cross product of middle digits b and b [(a$$\times$$c)+(a$$\times$$c)+(b$$\times$$b)] Step 4: get 2ab by criss-cross product of a and b [(a$$\times$$b)+(a$$\times$$b)] Step 5: get  $$\mathbf{a^{2}}$$ by multiplying right side digits [a$$\times$$a]

This can be written as:

Example: $$713^{2}$$
Step 1: Break the number such that a=7, b=1 and c=3
Step 2: Compute $$a^{2}$$ , ab, ac, bc and $$c^{2}$$ and write as shown in the updated formula.
Step 3: Notice the second row of the formula is obtained by repeating the second, third and fourth term.
Step 4: Compute $$b^{2}$$ and place it in the 3rd column below ac term.
Step 5: Now, add the terms taking care of the carry-forward in each step to obtain the square of the number.

So, $$713^{2}$$ = 508369