{"id":3972,"date":"2024-03-12T22:14:50","date_gmt":"2024-03-12T21:14:50","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&p=3972"},"modified":"2024-03-13T07:31:31","modified_gmt":"2024-03-13T06:31:31","password":"","slug":"square-root","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/square-root\/","title":{"rendered":"Square root"},"content":{"rendered":"\n

A square root of a number is the number which multiplied by itself results in the original number, so the square root of 4 is 2, the square root of 9 is 3, of 16 is 4 etc.<\/p>\n\n\n\n

This comes up mostly in the relationship between variance and standard deviation as the standard deviation is the square root of the variance.<\/p>\n\n\n\n

Details<\/h4>\n\n\n\n

The mathematical symbol for a square root is a symbol a bit like a tick mark so \\(\\sqrt{9}=3\\). I remember asking my late uncle what the symbol was seeing it in one of his engineering books. He said, rather haughtily, that it was a square root but I was none the wiser as we hadn’t yet come to that in school maths. I think I was 13 or 14 but that experience has clearly stuck with me!!<\/p>\n\n\n\n

The square root of 1 is 1, i.e. in algebra \\(\\sqrt{1}=1\\). The square root of a number larger than one is always smaller than the number, e.g. \\(\\sqrt{4}=2\\), \\(\\sqrt{9}=3\\) etc. That’s shown here.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The square root of a positive number smaller than one is larger than the number so \\(\\sqrt{\\frac{1}{4}}=\\frac{1}{2}\\). The square root of a negative number is impossible as squaring a negative number e.g. -2*-2 = +4 just as squaring a positive number results in a positive number, e.g. 2*2 = 4.<\/p>\n\n\n\n

Strictly speaking there are two square roots of any number because two identical numbers multiplied together result in a positive number so -2*-2 = 4 just as 2*2 = 4 so strictly there are two square roots of 4: \\(\\sqrt{4}=2\\) and \\(\\sqrt{4}=-2\\), or \\(\\sqrt{4}=\\pm2\\).<\/p>\n\n\n\n

Tangential<\/h4>\n\n\n\n

Actually, to mathematicians the square root of a negative number does exist but it’s an “imaginary number” so \\(\\sqrt{-9}=3i\\) where i is the square root of -1. That was a bit of a shock doing what was then “A level maths” at 17 but it did, as it has for generations of real mathematicians, then come to seem simple and rather wonderful. I hasten to say that I’m not a real mathematician! However, I think it made thinking about the psychoanalytic unconscious much easier to have had that exposure to imaginary numbers (a year or two before I discovered Freud!)<\/p>\n\n\n\n

Try also<\/h4>\n\n\n\n

Complex numbers
Imaginary numbers
Standard deviation (SD)
Variance<\/p>\n\n\n\n

Chapters<\/h4>\n\n\n\n

Not really addressed in the book.<\/p>\n\n\n\n

Online resources<\/h4>\n\n\n\n

Not yet.<\/p>\n\n\n\n

Dates<\/h4>\n\n\n\n

First created 12.iii.24.<\/p>\n","protected":false},"excerpt":{"rendered":"

A square root of a number is the number which multiplied by itself results in the original number, so the square root of 4 is 2, the square root of 9 is 3, of 16 is 4 etc. This comes up mostly in the relationship between variance and standard deviation as the standard deviation is … Continue reading Square root<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"doc_category":[18],"glossaries":[],"doc_tag":[],"knowledge_base":[],"class_list":["post-3972","docs","type-docs","status-publish","hentry","doc_category-om-book"],"year_month":"2026-04","word_count":380,"total_views":"1184","reactions":{"happy":"0","normal":"0","sad":"0"},"author_info":{"name":"chris","author_nicename":"chris","author_url":"https:\/\/www.psyctc.org\/psyctc\/author\/chris\/"},"doc_category_info":[{"term_name":"All OM book glossary entries","term_url":"https:\/\/www.psyctc.org\/psyctc\/glossary\/non-knowledgebase\/om-book\/"}],"doc_tag_info":[],"knowledge_base_info":[],"knowledge_base_slug":[],"_links":{"self":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3972","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/comments?post=3972"}],"version-history":[{"count":10,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3972\/revisions"}],"predecessor-version":[{"id":4005,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3972\/revisions\/4005"}],"wp:attachment":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/media?parent=3972"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_category?post=3972"},{"taxonomy":"glossaries","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/glossaries?post=3972"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_tag?post=3972"},{"taxonomy":"knowledge_base","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/knowledge_base?post=3972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}