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# Quick Calculations 1: Squaring numbers divisible by 5

How can we quickly square numbers divisible by 5?

Lets go into an example: $$145^2$$.

We split it into 2 parts : 14 and 5.

The last two digits are 25.

Then, the next succesive digits are $$14 \cdot 15$$, or $$14 \cdot (14+1)$$.

Therefore, $$145^2=21025$$.

Why does this work?

Note by David Lee
3 years, 8 months ago

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Simple. Take an $$n$$ digit number, where $$n\ge2$$, as $$10x+5$$. Thus, the number squared is $$(10x+5)^{2}$$ $$=$$ $$100x^{2} + 100x + 25$$. Since the coefficients of $$x^{2}$$ and $$x$$ are multiplied by $$100$$, the last two digits are $$25$$. Now the next digits are given by $$100(x)(x+1)$$, thus proving the property

- 3 years, 8 months ago

@David Lee, I knew that!

- 3 years, 8 months ago