# 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

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