Easily square numbers from 101 to 199.
Example
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Step 1
Square the last 2 digits.
{% scaleimage l306_step1.png %}
Step 2
Add the last 2 digits to the original number.
112 + 12 = 124
Step 3
Add two zeros to the end of step 2.
124 * 100 = 12400
Step 4
Add the results of step 1 and step 3.
12400 + 144 = 12544
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