{"id":240,"date":"2019-06-26T23:08:37","date_gmt":"2019-06-26T23:08:37","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=240"},"modified":"2020-01-03T19:36:17","modified_gmt":"2020-01-03T19:36:17","slug":"squares-ending-in-5","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/squares-ending-in-5\/","title":{"rendered":"Squares Ending in 5"},"content":{"rendered":"\n<p>Give me any 2 digit number that ends in 5, and I&#8217;ll square it in my head!&nbsp;<br>45<sup>2<\/sup>&nbsp;= 2025&nbsp;<br>85<sup>2<\/sup>&nbsp;= 7225, etc.<\/p>\n\n\n\n<p>There&#8217;s a quick way to do this: if the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>After telling the trick, have students see how fast they can square such numbers in their head, but doing several examples.<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>You may wish to assign the proof as a fun homework exercise: multiply (10N+5)(10N+5) and interpret! The trick works for larger numbers, too, although it may be harder to do this in your head. For instance 205<sup>2<\/sup>\u00a0= 42025, since 20*21=420. Also, you can combine this trick with other\u00a0lightning arithmetic\u00a0tricks. So 115<sup>2<\/sup>\u00a0= 13225, because 11*12 = 132, using the\u00a0Multiplication by 11\u00a0trick.<\/p>\n\n\n\n<p>The reference also contains more secrets of fast mental calculations.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Squares Ending in 5.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.<\/p>\n\n\n\n<p><strong>References:<\/strong><br>A. Benjamin and M. Shermer, <a href=\"http:\/\/www.amazon.com\/exec\/obidos\/ASIN\/0307338401\/ref=nosim\/mathfunfacts-20\">Secrets of Mental Math<\/a>, Three Rivers Press, 2006.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by: <\/strong>  <br>Francis Su <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Give me any 2 digit number that ends in 5, and I&#8217;ll square it in my head!&nbsp;452&nbsp;= 2025&nbsp;852&nbsp;= 7225, etc.&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[2,3,87],"class_list":["post-240","page","type-page","status-publish","hentry","tag-algebra","tag-easy","tag-lightning-arithmetic"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/240\/revisions"}],"predecessor-version":[{"id":1652,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/240\/revisions\/1652"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}