{"id":177,"date":"2024-08-27T08:34:13","date_gmt":"2024-08-27T08:34:13","guid":{"rendered":"https:\/\/kierunekmatura.pl\/blog\/?p=177"},"modified":"2025-08-01T20:29:40","modified_gmt":"2025-08-01T20:29:40","slug":"pierwiastkowanie","status":"publish","type":"post","link":"https:\/\/kierunekmatura.pl\/blog\/pierwiastkowanie\/","title":{"rendered":"Pierwiastkowanie"},"content":{"rendered":"\n<p>Wprowadzenie do pierwiastk\u00f3w i pot\u0119g u\u0142amkowych<\/p>\n\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPot\u0119ga u\u0142amkowa<\/span><\/h3>\r\n<p>\\(\\sqrt[n]{a} = a^{\\frac{1}{n}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{5} = 5^{\\frac{1}{2}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt[3]{6} = 6^{\\frac{1}{3}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPot\u0119ga u\u0142amkowa z licznikiem wi\u0119kszym od 1<\/span><\/h3>\r\n<p>\\(\\sqrt[n]{a^m} = a^{\\frac{m}{n}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\((\\sqrt[3]{4})^2 = 4^{\\frac{2}{3}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt[5]{7^4} = 7^{\\frac{4}{5}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPierwiastek z iloczynu<\/span><\/h3>\r\n<p>\\(\\sqrt{a} \\cdot \\sqrt{b} = \\sqrt{ab}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{2} \\cdot \\sqrt{3} = \\sqrt{6}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{5} \\cdot \\sqrt{7} = \\sqrt{35}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{5} \\cdot \\sqrt{5} = \\sqrt{25} = 5\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPierwiastek z pot\u0119gi<\/span><\/h3>\r\n<p>\\(\\sqrt[n]{a} \\cdot \\sqrt[n]{b} = \\sqrt[n]{ab}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{3} \\cdot \\sqrt{4} = \\sqrt{12}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt[5]{3} \\cdot \\sqrt[5]{4} = \\sqrt[5]{12}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPierwiastek z ilorazu<\/span><\/h3>\r\n<p>\\(\\sqrt{\\frac{a}{b}} = \\frac{\\sqrt{a}}{\\sqrt{b}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{\\frac{2}{3}} = \\frac{\\sqrt{2}}{\\sqrt{3}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt{\\frac{4}{9}} = \\frac{2}{3}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-note\">\r\n<h3 class=\"box-legend\"><span>\r\nPierwiastek z pot\u0119gi ilorazu<\/span><\/h3>\r\n<p>\\(\\sqrt[n]{\\frac{a}{b}} = \\frac{\\sqrt[n]{a}}{\\sqrt[n]{b}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt[3]{\\frac{5}{8}} = \\frac{\\sqrt[3]{5}}{\\sqrt[3]{8}}\\)<\/p>\n\r\n<\/div>\n\n<div class=\"box-example\">\r\n<h4 class=\"box-legend\"><span>Przyk\u0142ad<\/span><\/h4>\r\n<p>\\(\\sqrt[5]{\\frac{7}{10}} = \\frac{\\sqrt[5]{7}}{\\sqrt[5]{10}}\\)<\/p>\n\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Wprowadzenie do pierwiastk\u00f3w i pot\u0119g u\u0142amkowych<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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