{"id":9376,"date":"2010-04-13T17:05:42","date_gmt":"2010-04-13T17:05:42","guid":{"rendered":"http:\/\/www.driko.org\/blog\/2010\/04\/13\/square-large-numbers-in-your-head-quickly\/"},"modified":"2010-04-13T17:05:42","modified_gmt":"2010-04-13T17:05:42","slug":"square-large-numbers-in-your-head-quickly","status":"publish","type":"post","link":"https:\/\/www.driko.org\/blog\/2010\/04\/13\/square-large-numbers-in-your-head-quickly\/","title":{"rendered":"Square Large Numbers in Your Head Quickly"},"content":{"rendered":"

Square Large Numbers in Your Head Quickly<\/a><\/p>\n

\n

This just blew my mind:<\/p>\n

[W]hat’s 27 [squared]? Of course, the brute force way to do that is to calculate 27 x 27 which is a bit of a pain because it involves doing something like 27 x 20 + 27 x 7 = 540 + 189 = 729. But there’s a much faster way.<\/p><\/blockquote>\n

Observe that 272 = 30 x 24 + 32. Since you probably know that 32 = 9 this means you have to calculate 30 x 24 + 9 which is relatively easy because the multiplication involves a multiple of ten which means it’s really 3 x 24 and then add a zero.<\/p><\/blockquote>\n

So the rule is that if you want to square number X you first round it to the nearest multiple of 10, called that X + r, and then calculate X – r (i.e. round the same amount in the opposite direction). You calculate (X + r) x (X – r) and add back the square of the amount you rounded by, r2, which will be 1, 4, 9, 16 or 25.<\/p><\/blockquote>\n

I convinced myself with a simpler example: 12 squared. Round down to ten and an equal amount up to 14; square the amount you rounded (2) and add it to the product: 10*14 + 2^2 = 144. Cool…<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Square Large Numbers in Your Head Quickly This just blew my mind: [W]hat’s 27 [squared]? Of course, the brute force way to do that is to calculate 27 x 27 which is a bit of a pain because it involves doing something like 27 x 20 + 27 x 7 = 540 + 189 = … <\/p>\n

Continue reading “Square Large Numbers in Your Head Quickly”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"link","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-9376","post","type-post","status-publish","format-link","hentry","category-uncategorized","post_format-post-format-link"],"_links":{"self":[{"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/posts\/9376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/comments?post=9376"}],"version-history":[{"count":0,"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/posts\/9376\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/media?parent=9376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/categories?post=9376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.driko.org\/blog\/wp-json\/wp\/v2\/tags?post=9376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}