{"id":301,"date":"2019-06-26T23:30:25","date_gmt":"2019-06-26T23:30:25","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=301"},"modified":"2020-01-03T20:55:54","modified_gmt":"2020-01-03T20:55:54","slug":"squaring-numbers-between-40-and-60","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/squaring-numbers-between-40-and-60\/","title":{"rendered":"Squaring Numbers between 40 and 60"},"content":{"rendered":"\n

Here’s a quick way to square numbers between 40 and 60. You know the squares of 40, 50, and 60, right?<\/p>\n\n\n\n

So let’s show what to do for N=51 through 59. Write N as (50+R) for R between 1 and 9. Then N2<\/sup> will have first two digits (25+R) and last two digits R2<\/sup>. Thus: <\/p>\n\n\n\n

522<\/sup>= 2704,
582<\/sup>= 3364, <\/p>\n\n\n\n

since 27=25+2 and 33=25+8.<\/p>\n\n\n\n

The rule for N=41 through 49 is similar. Write N as (40+R) for R between 1 and 9. Then N2<\/sup> will have first two digits (15+R) and last two digits (10-R)2<\/sup>. So: <\/p>\n\n\n\n

422<\/sup>= 1764.
482<\/sup>= 2304.<\/p>\n\n\n\n

Presentation Suggestions:<\/strong>
This Fun Fact goes nicely with other lightning arithmetic tricks, such as Squaring Quickly and Squares Ending in 5. The reference gives many more secrets of mental math.<\/p>\n\n\n\n

The Math Behind the Fact:<\/strong>
These “rules” are easy to check by noting, for example, that<\/p>\n\n\n\n

(50+R)2<\/sup> = 2500+100*R+R2<\/sup>.<\/p>\n\n\n\n

And since (40+R)2<\/sup>\u00a0= (50 – (10-R) )2<\/sup>, we have <\/p>\n\n\n\n

(50 – (10-R) )2<\/sup>\u00a0= 2500 -100*(10-R)+(10-R)2<\/sup>\u00a0= 1500 +100*R+(10-R)2<\/sup>.<\/p>\n\n\n\n

How to Cite this Page:<\/strong> 
Su, Francis E., et al. “Squaring Numbers between 40 and 60.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n

References:<\/strong>
A. Benjamin and M. Shermer, Secrets of Mental Math<\/a>, Three Rivers Press, 2006<\/p>\n\n\n\n

Fun Fact suggested by: <\/strong>
Francis Su <\/p>\n","protected":false},"excerpt":{"rendered":"

Here’s a quick way to square numbers between 40 and 60. You know the squares of 40, 50, and 60,...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[2,3,168,87],"class_list":["post-301","page","type-page","status-publish","hentry","tag-algebra","tag-easy","tag-fast-mental-math","tag-lightning-arithmetic"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/301","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=301"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/301\/revisions"}],"predecessor-version":[{"id":1654,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/301\/revisions\/1654"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=301"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}