Problem
NT-B1-M12-P020 Set 4. Square Ending in \(5\)
#20
★★★☆☆ Level 3 of 5
Prove that if the square of a positive integer ends in digit \(5\), then its last two digits are \(25\).
A number whose square ends in \(5\) itself ends in \(5\).
Let the number be \(10a+5\). Then \((10a+5)^2=100a^2+100a+25=100a(a+1)+25\). Thus the last two digits of the square are \(25\).
Small but good digit-representation proof.