# Square of three digit number whose digits are same

Let us consider the 3-digit number as aaa. Let’s see how the square of the number looks like:

Examples:

$$111^{2}$$ = $$1^{2}$$ / 2$$(1^{2})$$ / 3$$(1^{2})$$ / 2$$(1^{2})$$ / $$1^{2}$$ = 1 / 2 / 3 / 2 / 1 = 12321

$$222^{2}$$ = $$2^{2}$$ / 2$$(2^{2})$$ / 3$$(2^{2})$$ / 2$$(2^{2})$$ / $$2^{2}$$ = 4 / 8 / 12 / 8 / 4 = 49284

For detailed explanation check below:

$$666^{2}$$ = $$6^{2}$$ / 2$$(6^{2})$$ / 3$$(6^{2})$$ / 2$$(6^{2})$$ / $$6^{2}$$ = 36 / 72 / 108 / 72 / 36 = 443556

For detailed explanation check below: