{"id":2553,"date":"2021-03-11T19:17:03","date_gmt":"2021-03-11T18:17:03","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=2553"},"modified":"2021-03-11T20:30:15","modified_gmt":"2021-03-11T19:30:15","slug":"cuadrados-perfectos-invertibles","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/cuadrados-perfectos-invertibles\/","title":{"rendered":"Cuadrados perfectos invertibles"},"content":{"rendered":"

Un n\u00famero cuadrado perfecto<\/strong> es un n\u00famero que tiene ra\u00edz cuadrada exacta.<\/span><\/p>\n

Hay cuadrados perfectos que al invertir sus cifras tambi\u00e9n dan lugar a otro cuadrado perfecto. Por ejemplo, los cuadrados perfectos capic\u00faas, que ya se han tratado en una entrada anterior.<\/span><\/p>\n

\u2022 En la mayor\u00eda de los casos, las ra\u00edces de los dos cuadrados perfectos invertidos son tambi\u00e9n n\u00fameros con sus cifras invertidas. En la tabla se muestran los n\u00fameros menor (no capic\u00faa) y mayor con 2, 3, 4, 5, 6 y 7 cifras que verifican esta propiedad:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
N\u00famero<\/span><\/strong><\/td>\nCuadrado<\/span><\/strong><\/td>\nInvertido<\/span><\/strong><\/td>\nRa\u00edz cuadrada<\/span><\/strong><\/td>\n<\/tr>\n
12<\/span><\/strong><\/td>\n144<\/span><\/td>\n441<\/span><\/td>\n21<\/span><\/strong><\/td>\n<\/tr>\n
31<\/span><\/strong><\/td>\n961<\/span><\/td>\n169<\/span><\/td>\n13<\/span><\/strong><\/td>\n<\/tr>\n
102<\/span><\/strong><\/td>\n10404<\/span><\/td>\n40401<\/span><\/td>\n201<\/span><\/strong><\/td>\n<\/tr>\n
311<\/span><\/strong><\/td>\n96721<\/span><\/td>\n12769<\/span><\/td>\n113<\/span><\/strong><\/td>\n<\/tr>\n
1002<\/span><\/strong><\/td>\n1001004<\/span><\/td>\n4001001<\/span><\/td>\n2001<\/span><\/strong><\/td>\n<\/tr>\n
3111<\/span><\/strong><\/td>\n9678321<\/span><\/td>\n1238769<\/span><\/td>\n1113<\/span><\/strong><\/td>\n<\/tr>\n
10002<\/span><\/strong><\/td>\n100040004<\/span><\/td>\n400040001<\/span><\/td>\n20001<\/span><\/strong><\/td>\n<\/tr>\n
31111<\/span><\/strong><\/td>\n967894321<\/span><\/td>\n123498769<\/span><\/td>\n11113<\/span><\/strong><\/td>\n<\/tr>\n
100002<\/span><\/strong><\/td>\n10000400004<\/span><\/td>\n40000100001<\/span><\/td>\n200001<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
211111<\/span><\/strong><\/td>\n44567854321<\/span><\/td>\n12345876544<\/span><\/td>\n111112<\/span><\/strong><\/td>\n<\/tr>\n
1000002<\/span><\/strong><\/td>\n1000004000002<\/span><\/td>\n4000004000001<\/span><\/td>\n2000001<\/span><\/strong><\/td>\n<\/tr>\n
2111111<\/span><\/strong><\/td>\n 4456789654321<\/span><\/td>\n1234569876544<\/span><\/td>\n1111112<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\u2022 Pero en otros casos, los dos cuadrados perfectos invertidos se obtienen de n\u00fameros con las cifras distintas. Por ejemplo:
\n<\/span><\/p>\n\n\n\n\n\n
N\u00famero<\/span><\/strong><\/td>\nCuadrado<\/span><\/strong><\/td>\nInvertido<\/span><\/strong><\/td>\nRa\u00edz cuadrada<\/span><\/strong><\/td>\n<\/tr>\n
33<\/span><\/strong><\/td>\n1089<\/span><\/td>\n9801<\/span><\/td>\n99<\/span><\/strong><\/td>\n<\/tr>\n
3168<\/span><\/strong><\/td>\n10036224<\/span><\/td>\n42263001<\/span><\/td>\n6501<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Un n\u00famero cuadrado perfecto es un n\u00famero que tiene ra\u00edz cuadrada exacta. Hay cuadrados perfectos que al invertir sus cifras tambi\u00e9n dan lugar a otro cuadrado perfecto. Por ejemplo, los cuadrados perfectos capic\u00faas, que...<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/2553"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=2553"}],"version-history":[{"count":10,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/2553\/revisions"}],"predecessor-version":[{"id":2563,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/2553\/revisions\/2563"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=2553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=2553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=2553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}