{"id":2857,"date":"2022-09-03T08:25:57","date_gmt":"2022-09-03T12:25:57","guid":{"rendered":"https:\/\/josmfs.net\/?p=2857"},"modified":"2026-02-20T21:03:50","modified_gmt":"2026-02-21T02:03:50","slug":"square-root-minimum","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/09\/03\/square-root-minimum\/","title":{"rendered":"Square Root Minimum"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2855\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/09\/Square-Root-Minimum-Fig2.jpg\" alt=\"\" width=\"256\" height=\"145\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/09\/Square-Root-Minimum-Fig2.jpg 455w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/09\/Square-Root-Minimum-Fig2-300x170.jpg 300w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/>This seemingly impossible <a href=\"https:\/\/mindyourdecisions.com\/blog\/2022\/06\/07\/minimum-of-sum-of-square-roots\/\">problem<\/a> from Presh Talwalkar turned out to be quite solvable upon reflection.<\/p>\n<p>&#8220;A similar question was given to students in Thailand. For real numbers <em>x<\/em>, <em>y<\/em>, what is the minimum value of<\/p>\n<p style=\"text-align: center;\">\u221a((<em>x<\/em> \u2013 4)<sup>2<\/sup> + (<em>y<\/em> \u2013 10)<sup>2<\/sup>) + \u221a((<em>x<\/em> \u2013 44)<sup>2<\/sup> + (<em>y<\/em> \u2013 19)<sup>2<\/sup>)&#8221;<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Square-Root-Minimum-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/09\/Square-Root-Minimum-220608.pdf\">Square Root Minimum<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This seemingly impossible problem from Presh Talwalkar turned out to be quite solvable upon reflection. &#8220;A similar question was given to students in Thailand. For real numbers x, y, what is the minimum value of \u221a((x \u2013 4)2 + (y \u2013 10)2) + \u221a((x \u2013 44)2 + (y \u2013 19)2)&#8221; Answer. See the Square Root [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[153,13,17],"class_list":["post-2857","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-optimization","tag-plane-geometry","tag-presh-talwalkar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2857","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2857"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2857\/revisions"}],"predecessor-version":[{"id":3599,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2857\/revisions\/3599"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2857"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2857"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2857"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}