Question

Find the square of 106 without direct multiplication.

Answer 1

Take the difference of given number and 100, then add this to the given number.
$(106-100)=6$ and $106+6=112$

Find the square of difference of the given number and 100.
${(106-100)}^2=36$

Multiply result of first step with 100 and add result of second step in that.
So $112\times 100=11200+36=11236$
Hence, the square of 106 is 11236.

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