{"id":1091,"date":"2022-03-07T18:34:20","date_gmt":"2022-03-07T18:34:20","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/vlastnosti-odmocni\/"},"modified":"2022-03-07T20:08:46","modified_gmt":"2022-03-07T20:08:46","slug":"vlastnosti-odmocnin","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/vlastnosti-odmocnin\/","title":{"rendered":"Vlastnosti odmocnin"},"content":{"rendered":"<ul>\n<li>Odmoc\u0148ov\u00e1n\u00ed je \u010d\u00e1ste\u010dn\u011b inverzn\u00ed operac\u00ed k umoc\u0148ov\u00e1n\u00ed.<\/li>\n<li><strong>V\u00fdsledkem odmoc\u0148ov\u00e1n\u00ed je odmocnina.<\/strong><\/li>\n<li>Nej\u010dast\u011bji se pou\u017e\u00edv\u00e1<strong> druh\u00e1 odmocnina<\/strong>, kter\u00e1 se zna\u010d\u00ed: <strong>\u221a<\/strong>, p\u0159i\u010dem\u017e plat\u00ed, \u017ee: $$\\sqrt{a}\\cdot\\sqrt{a}={a}$$ neboli $${(\\sqrt{a})}^{2}={a}$$ $${(\\sqrt{6})}^{2}={6}$$<\/li>\n<li>P\u0159\u00edklady druh\u00fdch odmocnin: $$\\sqrt{25}={5}$$ $$\\sqrt{64}={8}$$<\/li>\n<li>Podobn\u011b jako u mocnin, i odmocniny mohou b\u00fdt v\u00edcen\u00e1sobn\u00e9, nap\u0159\u00edklad t\u0159et\u00ed odmocnina, \u010dtvrt\u00e1, p\u00e1t\u00e1 a tak d\u00e1le, p\u0159i\u010dem\u017e plat\u00ed n\u00e1sleduj\u00edc\u00ed vztahy: $${(\\sqrt[3]{x})}^{3}=x$$ $$({\\sqrt[4]{x})}^{4}=x$$ $${(\\sqrt[5]{x})}^{5}=x$$<\/li>\n<li>Z\u00e1rove\u0148 plat\u00ed n\u011bkolik z\u00e1kladn\u00edch pravidel, vzorc\u016f a vztah\u016f:<\/li>\n<\/ul>\n<p>$$\\sqrt{a}={a}^\\frac{1}{2}$$<\/p>\n<p>$$\\sqrt[n]{0}=0$$<\/p>\n<p>$$\\sqrt[n]{1}=1$$<\/p>\n<p><em><strong>a,b\u22650: <\/strong><\/em>$$\\sqrt[n]{{a}\\cdot{b}}=\\sqrt[n]{a}\\cdot\\sqrt[n]{b}$$<\/p>\n<p><em><strong>a,b\u22650:\u00a0<\/strong><\/em>$$\\sqrt[n]{\\frac{a}{b}}=\\frac{\\sqrt[n]{a}}{\\sqrt[n]{b}}$$<\/p>\n<p><em><strong>a&gt;0:<\/strong><\/em>$${a}^{\\frac{m}{n}}=\\sqrt[n]{{a}^{m}}$$<\/p>\n<p><em><strong>a&gt;0: <\/strong><\/em>$$\\sqrt[n]{\\sqrt[m]{a}}=\\sqrt[{n}\\cdot{m}]{a}$$<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1091","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Vlastnosti odmocnin | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/vlastnosti-odmocnin\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Vlastnosti odmocnin | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Odmoc\u0148ov\u00e1n\u00ed je \u010d\u00e1ste\u010dn\u011b inverzn\u00ed operac\u00ed k umoc\u0148ov\u00e1n\u00ed. V\u00fdsledkem odmoc\u0148ov\u00e1n\u00ed je odmocnina. Nej\u010dast\u011bji se pou\u017e\u00edv\u00e1 druh\u00e1 odmocnina, kter\u00e1 se zna\u010d\u00ed: \u221a, p\u0159i\u010dem\u017e plat\u00ed, \u017ee: $$sqrt{a}cdotsqrt{a}={a}$$ neboli $${(sqrt{a})}^{2}={a}$$ $${(sqrt{6})}^{2}={6}$$ P\u0159\u00edklady druh\u00fdch odmocnin: $$sqrt{25}={5}$$ $$sqrt{64}={8}$$ Podobn\u011b jako u mocnin, i odmocniny mohou b\u00fdt v\u00edcen\u00e1sobn\u00e9, nap\u0159\u00edklad t\u0159et\u00ed odmocnina, \u010dtvrt\u00e1, p\u00e1t\u00e1 a tak d\u00e1le, p\u0159i\u010dem\u017e plat\u00ed n\u00e1sleduj\u00edc\u00ed vztahy: $${(sqrt[3]{x})}^{3}=x$$ $$({sqrt[4]{x})}^{4}=x$$ ... 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V\u00fdsledkem odmoc\u0148ov\u00e1n\u00ed je odmocnina. Nej\u010dast\u011bji se pou\u017e\u00edv\u00e1 druh\u00e1 odmocnina, kter\u00e1 se zna\u010d\u00ed: \u221a, p\u0159i\u010dem\u017e plat\u00ed, \u017ee: $$sqrt{a}cdotsqrt{a}={a}$$ neboli $${(sqrt{a})}^{2}={a}$$ $${(sqrt{6})}^{2}={6}$$ P\u0159\u00edklady druh\u00fdch odmocnin: $$sqrt{25}={5}$$ $$sqrt{64}={8}$$ Podobn\u011b jako u mocnin, i odmocniny mohou b\u00fdt v\u00edcen\u00e1sobn\u00e9, nap\u0159\u00edklad t\u0159et\u00ed odmocnina, \u010dtvrt\u00e1, p\u00e1t\u00e1 a tak d\u00e1le, p\u0159i\u010dem\u017e plat\u00ed n\u00e1sleduj\u00edc\u00ed vztahy: $${(sqrt[3]{x})}^{3}=x$$ $$({sqrt[4]{x})}^{4}=x$$ ... 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