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",[567,1814,1816,1832],{"className":1815},[570],[567,1817,1819],{"className":1818},[574],[576,1820,1821],{"xmlns":578},[580,1822,1823,1829],{},[583,1824,1825],{},[1121,1826,1827],{},[1124,1828,1131],{},[590,1830,1831],{"encoding":592},"\\sqrt{2}",[567,1833,1835],{"className":1834,"ariaHidden":597},[596],[567,1836,1838,1842],{"className":1837},[601],[567,1839],{"className":1840,"style":1841},[605],"height:1.04em;vertical-align:-0.1328em;",[567,1843,1845],{"className":1844},[610,714],[567,1846,1848,1881],{"className":1847},[689,690],[567,1849,1851,1878],{"className":1850},[694],[567,1852,1854,1866],{"className":1853,"style":1197},[698],[567,1855,1857,1860],{"className":1856,"style":763},[762],[567,1858],{"className":1859,"style":707},[706],[567,1861,1863],{"className":1862,"style":770},[610],[567,1864,1131],{"className":1865},[610],[567,1867,1868,1871],{"style":1212},[567,1869],{"className":1870,"style":707},[706],[567,1872,1874],{"className":1873,"style":784},[783],[786,1875,1876],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,1877],{"d":796},[567,1879,801],{"className":1880},[800],[567,1882,1884],{"className":1883},[694],[567,1885,1887],{"className":1886,"style":1232},[698],[567,1888],{},", 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2",[567,1921,1923,1987,2049],{"className":1922,"ariaHidden":597},[596],[567,1924,1926,1929,1976,1980,1984],{"className":1925},[601],[567,1927],{"className":1928,"style":1841},[605],[567,1930,1932],{"className":1931},[610,714],[567,1933,1935,1968],{"className":1934},[689,690],[567,1936,1938,1965],{"className":1937},[694],[567,1939,1941,1953],{"className":1940,"style":1197},[698],[567,1942,1944,1947],{"className":1943,"style":763},[762],[567,1945],{"className":1946,"style":707},[706],[567,1948,1950],{"className":1949,"style":770},[610],[567,1951,1131],{"className":1952},[610],[567,1954,1955,1958],{"style":1212},[567,1956],{"className":1957,"style":707},[706],[567,1959,1961],{"className":1960,"style":784},[783],[786,1962,1963],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,1964],{"d":796},[567,1966,801],{"className":1967},[800],[567,1969,1971],{"className":1970},[694],[567,1972,1974],{"className":1973,"style":1232},[698],[567,1975],{},[567,1977],{"className":1978,"style":1979},[928],"margin-right:0.2222em;",[567,1981,1908],{"className":1982},[1983],"mbin",[567,1985],{"className":1986,"style":1979},[928],[567,1988,1990,1993,2040,2043,2046],{"className":1989},[601],[567,1991],{"className":1992,"style":1841},[605],[567,1994,1996],{"className":1995},[610,714],[567,1997,1999,2032],{"className":1998},[689,690],[567,2000,2002,2029],{"className":2001},[694],[567,2003,2005,2017],{"className":2004,"style":1197},[698],[567,2006,2008,2011],{"className":2007,"style":763},[762],[567,2009],{"className":2010,"style":707},[706],[567,2012,2014],{"className":2013,"style":770},[610],[567,2015,1131],{"className":2016},[610],[567,2018,2019,2022],{"style":1212},[567,2020],{"className":2021,"style":707},[706],[567,2023,2025],{"className":2024,"style":784},[783],[786,2026,2027],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,2028],{"d":796},[567,2030,801],{"className":2031},[800],[567,2033,2035],{"className":2034},[694],[567,2036,2038],{"className":2037,"style":1232},[698],[567,2039],{},[567,2041],{"className":2042,"style":929},[928],[567,2044,651],{"className":2045},[933],[567,2047],{"className":2048,"style":929},[928],[567,2050,2052,2055],{"className":2051},[601],[567,2053],{"className":2054,"style":1393},[605],[567,2056,1131],{"className":2057},[610]," ist:",[567,2060,2062],{"className":2061},[616],[567,2063,2065,2116],{"className":2064},[570],[567,2066,2068],{"className":2067},[574],[576,2069,2070],{"xmlns":578,"display":625},[580,2071,2072,2113],{},[583,2073,2074,2083,2085,2103,2105],{},[631,2075,2076,2079],{},[1124,2077,2078],{},"1",[1121,2080,2081],{},[1124,2082,1131],{},[649,2084,651],{},[631,2086,2087,2091],{},[1121,2088,2089],{},[1124,2090,1131],{},[583,2092,2093,2097,2099],{},[1121,2094,2095],{},[1124,2096,1131],{},[649,2098,1908],{},[1121,2100,2101],{},[1124,2102,1131],{},[649,2104,651],{},[631,2106,2107,2111],{},[1121,2108,2109],{},[1124,2110,1131],{},[1124,2112,1131],{},[590,2114,2115],{"encoding":592},"\\frac{1}{\\sqrt{2}} = \\frac{\\sqrt{2}}{\\sqrt{2} \\cdot \\sqrt{2}} = 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\\frac{1}{\\sqrt{b}}",[567,2633,2635,2909],{"className":2634,"ariaHidden":597},[596],[567,2636,2638,2642,2859,2862,2906],{"className":2637},[601],[567,2639],{"className":2640,"style":2641},[605],"height:1.6684em;vertical-align:-0.6304em;",[567,2643,2645,2648,2856],{"className":2644},[610],[567,2646],{"className":2647},[681,682],[567,2649,2651],{"className":2650},[631],[567,2652,2654,2847],{"className":2653},[689,690],[567,2655,2657,2844],{"className":2656},[694],[567,2658,2661,2777,2785],{"className":2659,"style":2660},[698],"height:1.038em;",[567,2662,2664,2667],{"style":2663},"top:-2.5335em;",[567,2665],{"className":2666,"style":707},[706],[567,2668,2671],{"className":2669},[739,740,2670,742],"size3",[567,2672,2674,2724,2727],{"className":2673},[610,742],[567,2675,2677],{"className":2676},[610,714,742],[567,2678,2680,2715],{"className":2679},[689,690],[567,2681,2683,2712],{"className":2682},[694],[567,2684,2687,2699],{"className":2685,"style":2686},[698],"height:0.8059em;",[567,2688,2690,2693],{"className":2689,"style":763},[762],[567,2691],{"className":2692,"style":707},[706],[567,2694,2696],{"className":2695,"style":770},[610,742],[567,2697,638],{"className":2698},[610,611,742],[567,2700,2702,2705],{"style":2701},"top:-2.7659em;",[567,2703],{"className":2704,"style":707},[706],[567,2706,2708],{"className":2707,"style":784},[783,742],[786,2709,2710],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,2711],{"d":796},[567,2713,801],{"className":2714},[800],[567,2716,2718],{"className":2717},[694],[567,2719,2722],{"className":2720,"style":2721},[698],"height:0.2341em;",[567,2723],{},[567,2725,2612],{"className":2726},[1983,742],[567,2728,2730],{"className":2729},[610,714,742],[567,2731,2733,2768],{"className":2732},[689,690],[567,2734,2736,2765],{"className":2735},[694],[567,2737,2740,2752],{"className":2738,"style":2739},[698],"height:0.9378em;",[567,2741,2743,2746],{"className":2742,"style":763},[762],[567,2744],{"className":2745,"style":707},[706],[567,2747,2749],{"className":2748,"style":770},[610,742],[567,2750,645],{"className":2751},[610,611,742],[567,2753,2755,2758],{"style":2754},"top:-2.8978em;",[567,2756],{"className":2757,"style":707},[706],[567,2759,2761],{"className":2760,"style":784},[783,742],[786,2762,2763],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,2764],{"d":796},[567,2766,801],{"className":2767},[800],[567,2769,2771],{"className":2770},[694],[567,2772,2775],{"className":2773,"style":2774},[698],"height:0.1022em;",[567,2776],{},[567,2778,2779,2782],{"style":813},[567,2780],{"className":2781,"style":707},[706],[567,2783],{"className":2784,"style":821},[820],[567,2786,2788,2791],{"style":2787},"top:-3.4739em;",[567,2789],{"className":2790,"style":707},[706],[567,2792,2794],{"className":2793},[739,740,2670,742],[567,2795,2797],{"className":2796},[610,742],[567,2798,2800],{"className":2799},[610,714,742],[567,2801,2803,2836],{"className":2802},[689,690],[567,2804,2806,2833],{"className":2805},[694],[567,2807,2809,2821],{"className":2808,"style":2686},[698],[567,2810,2812,2815],{"className":2811,"style":763},[762],[567,2813],{"className":2814,"style":707},[706],[567,2816,2818],{"className":2817,"style":770},[610,742],[567,2819,638],{"className":2820},[610,611,742],[567,2822,2823,2826],{"style":2701},[567,2824],{"className":2825,"style":707},[706],[567,2827,2829],{"className":2828,"style":784},[783,742],[786,2830,2831],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,2832],{"d":796},[567,2834,801],{"className":2835},[800],[567,2837,2839],{"className":2838},[694],[567,2840,2842],{"className":2841,"style":2721},[698],[567,2843],{},[567,2845,801],{"className":2846},[800],[567,2848,2850],{"className":2849},[694],[567,2851,2854],{"className":2852,"style":2853},[698],"height:0.6304em;",[567,2855],{},[567,2857],{"className":2858},[924,682],[567,2860],{"className":2861,"style":929},[928],[567,2863,2865,2899,2903],{"className":2864},[933],[567,2866,2868],{"className":2867},[933],[567,2869,2872],{"className":2870},[610,2871],"vbox",[567,2873,2876],{"className":2874},[2875],"thinbox",[567,2877,2880,2884,2895],{"className":2878},[2879],"rlap",[567,2881],{"className":2882,"style":2883},[605],"height:0.8889em;vertical-align:-0.1944em;",[567,2885,2888],{"className":2886},[2887],"inner",[567,2889,2891],{"className":2890},[610],[567,2892,2894],{"className":2893},[933],"",[567,2896],{"className":2897},[2898],"fix",[567,2900],{"className":2901},[928,2902],"nobreak",[567,2904,651],{"className":2905},[933],[567,2907],{"className":2908,"style":929},[928],[567,2910,2912,2916],{"className":2911},[601],[567,2913],{"className":2914,"style":2915},[605],"height:1.3831em;vertical-align:-0.538em;",[567,2917,2919,2922,3028],{"className":2918},[610],[567,2920],{"className":2921},[681,682],[567,2923,2925],{"className":2924},[631],[567,2926,2928,3019],{"className":2927},[689,690],[567,2929,2931,3016],{"className":2930},[694],[567,2932,2935,2993,3001],{"className":2933,"style":2934},[698],"height:0.8451em;",[567,2936,2937,2940],{"style":2663},[567,2938],{"className":2939,"style":707},[706],[567,2941,2943],{"className":2942},[739,740,2670,742],[567,2944,2946],{"className":2945},[610,742],[567,2947,2949],{"className":2948},[610,714,742],[567,2950,2952,2985],{"className":2951},[689,690],[567,2953,2955,2982],{"className":2954},[694],[567,2956,2958,2970],{"className":2957,"style":2739},[698],[567,2959,2961,2964],{"className":2960,"style":763},[762],[567,2962],{"className":2963,"style":707},[706],[567,2965,2967],{"className":2966,"style":770},[610,742],[567,2968,645],{"className":2969},[610,611,742],[567,2971,2972,2975],{"style":2754},[567,2973],{"className":2974,"style":707},[706],[567,2976,2978],{"className":2977,"style":784},[783,742],[786,2979,2980],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,2981],{"d":796},[567,2983,801],{"className":2984},[800],[567,2986,2988],{"className":2987},[694],[567,2989,2991],{"className":2990,"style":2774},[698],[567,2992],{},[567,2994,2995,2998],{"style":813},[567,2996],{"className":2997,"style":707},[706],[567,2999],{"className":3000,"style":821},[820],[567,3002,3004,3007],{"style":3003},"top:-3.394em;",[567,3005],{"className":3006,"style":707},[706],[567,3008,3010],{"className":3009},[739,740,2670,742],[567,3011,3013],{"className":3012},[610,742],[567,3014,2078],{"className":3015},[610,742],[567,3017,801],{"className":3018},[800],[567,3020,3022],{"className":3021},[694],[567,3023,3026],{"className":3024,"style":3025},[698],"height:0.538em;",[567,3027],{},[567,3029],{"className":3030},[924,682],". Im Nenner ist ",[567,3033,3035,3051],{"className":3034},[570],[567,3036,3038],{"className":3037},[574],[576,3039,3040],{"xmlns":578},[580,3041,3042,3048],{},[583,3043,3044],{},[1121,3045,3046],{},[586,3047,638],{},[590,3049,3050],{"encoding":592},"\\sqrt{a}",[567,3052,3054],{"className":3053,"ariaHidden":597},[596],[567,3055,3057,3061],{"className":3056},[601],[567,3058],{"className":3059,"style":3060},[605],"height:1.04em;vertical-align:-0.2397em;",[567,3062,3064],{"className":3063},[610,714],[567,3065,3067,3100],{"className":3066},[689,690],[567,3068,3070,3097],{"className":3069},[694],[567,3071,3073,3085],{"className":3072,"style":871},[698],[567,3074,3076,3079],{"className":3075,"style":763},[762],[567,3077],{"className":3078,"style":707},[706],[567,3080,3082],{"className":3081,"style":770},[610],[567,3083,638],{"className":3084},[610,611],[567,3086,3087,3090],{"style":886},[567,3088],{"className":3089,"style":707},[706],[567,3091,3093],{"className":3092,"style":784},[783],[786,3094,3095],{"xmlns":788,"width":789,"height":790,"viewBox":791,"preserveAspectRatio":792},[794,3096],{"d":796},[567,3098,801],{"className":3099},[800],[567,3101,3103],{"className":3102},[694],[567,3104,3106],{"className":3105,"style":906},[698],[567,3107],{}," kein gemeinsamer Faktor, der Bruch lässt sich so nicht kürzen.",[2583,3110,3111],{},"Beim Erweitern nur den Nenner multiplizieren. Zähler und Nenner müssen mit demselben Faktor erweitert werden.",{"title":3113,"searchDepth":3114,"depth":3114,"links":3115},"",2,[3116,3117,3118],{"id":560,"depth":3114,"text":561},{"id":1101,"depth":3114,"text":1102},{"id":2577,"depth":3114,"text":2578},[3120,3123,3125,3128],{"lhs":3121,"rhs":3122},"sqrt(a) \u002F sqrt(b)","sqrt(a\u002Fb)",{"lhs":3124,"rhs":1143},"sqrt(72) \u002F sqrt(2)",{"lhs":3126,"rhs":3127},"sqrt(9\u002F25)","3\u002F5",{"lhs":3129,"rhs":3130},"1 \u002F sqrt(2)","sqrt(2) \u002F 2","a \\geq 0,\\ b > 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\geq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","root-quotient-rule","\\frac{\\sqrt{a}}{\\sqrt{b}} = \\sqrt{\\frac{a}{b}}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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