document.write( "Question 106191: Show that a quick way to square a positive integer ending in five is to place twenty-five after the product of the number formed by the digits preceding the five and the next integer. for example, 65(squared) = 4225 [6x7 (the next integer) =42, then tack on 25] and 125(squared) = 15,625 [12x13 (the next integer) = 156, then tack on 25]. \n" ); document.write( "

Algebra.Com's Answer #77300 by Fombitz(32388) $\"\"$ $\"About$

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$\"%28a%2B5%29%5E2=a%5E2%2B10a%2B25\"$ Expand the right hand side.
\n" ); document.write( " $\"%28a%2B5%29%5E2=%28a%5E2%2B10a%29%2B25\"$
\n" ); document.write( " $\"%28a%2B5%29%5E2=10%2A%28a%5E2%2F10%2Ba%29%2B25\"$ Distributive property.
\n" ); document.write( " $\"%28a%2B5%29%5E2=10%2A10%2A%28a%5E2%2F10%5E2%2Ba%2F10%29%2B25\"$ Distributive property.
\n" ); document.write( " $\"%28a%2B5%29%5E2=10%2A10%2A%28a%2F10%29%2A%28a%2F10%2B1%29%2B25\"$ Distributive property.
\n" ); document.write( "Example:
\n" ); document.write( " $\"a=60\"$
\n" ); document.write( " $\"a%2F10=6\"$
\n" ); document.write( " $\"a%2F10%2B1=7\"$
\n" ); document.write( " $\"%28a%2B5%29%5E2=10%2A10%2A%28a%2F10%29%2A%28a%2F10%2B1%29%2B25\"$
\n" ); document.write( " $\"%2860%2B5%29%5E2=10%2A10%2A%2860%2F10%29%2A%2860%2F10%2B1%29%2B25\"$
\n" ); document.write( " $\"65%5E2=100%2A6%2A7%2B25\"$
\n" ); document.write( " $\"4225=4225\"$
\n" ); document.write( " \n" ); document.write( "

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