The sutra (formula) that empowers me to do so at ease is "Ekadhikena Purevena", meaning by one more than the previous one.
To calculate square of any number ending in 5, say z5 is z(z+1)|25, ie, multiply z by z+1 and attach 25 next to it.
For example, 752 is:
752 = 7(7+1)|25 = 5625
Simple and powerful, isn't it? Now, let us see what goes behind it. It's simple algebra.
(10x + 5)2 = 100x2 + 100x + 25 = 100x(x+1) + 25 = x(x+1)|25
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