Many folks go to the trouble to memorize squares of numbers up to about 20 or even 30.
12² = 12×12 = 144
10² = 10×10 = 100
36² = 36×36 = 900 +360 +36 = 1296
81² = 81×81 = 6400 +160 +1 = 6561
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In general, (a+b)² = a² +2ab +b².
You can use that here. For example, 36² = (30 +6)² = 30² +2×30×6 +6²
Of course 30² = (3×10)² = 3²×10² = 9×100.
and 2×30×6 = 2×3×6×10 = 36×10
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Many calculators have an x² key that will give you the answer directly.