Răspuns :
Răspuns
5. √16/25 = 4/5 ; √81/64 = 9/8 ; √9/49 = 3/7 ; √144/169 = 12/13 ; √100/289 = 10/17 ; √256/225 = 16/15 ; √196/289 = 14/17 ; √625/324 = 25/18 ; √169/256 = 13/16 ; √144/1225 = 12/35 ; √196/324 = 14/18 ;
√2 7/9 = √25/9 = 5/3 ; √5 19/25 = √144/25 = 12/5 ; √1 32/49 =√81/49 = 9/7 ;
6. √11 1/9 = √100/9 = 10/3 ; √7 9/16 = √121/16 = 11/4 ; √4 25/36 = √169/36 = 13/6 ;
√4 33/64 = √289/64 = 17/8 ; √20 1/4 = √121/4 = 11/2 ; √7 21/25 = √196/25 = 14/5 ; √6 30/49 = √324/49 = 18/7 ;
[tex]5) \\ \\ a) \sqrt{ \frac{16}{25} } = \frac{ \sqrt{16} }{ \sqrt{25} } = \frac{4}{5}[/tex]
[tex]b) \sqrt{ \frac{81}{64} } = \frac{ \sqrt{81} }{ \sqrt{64} } = \frac{9}{8} [/tex]
[tex]c) \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]
[tex]d) \sqrt{ \frac{144}{169} } = \frac{ \sqrt{144} }{ \sqrt{169} } = \frac{12}{13} [/tex]
[tex]e) \sqrt{ \frac{100}{289} } = \frac{ \sqrt{100} }{ \sqrt{289} } = \frac{10}{17} [/tex]
[tex]f) \sqrt{ \frac{256}{225} } = \frac{ \sqrt{256} }{ \sqrt{225} } = \frac{16}{15} [/tex]
[tex]g) \sqrt{ \frac{196}{289} } = \frac{ \sqrt{196} }{ \sqrt{289} } = \frac{14}{17} [/tex]
[tex]h) \sqrt{ \frac{625}{324} } = \frac{ \sqrt{625} }{ \sqrt{324} } = \frac{25}{18} [/tex]
[tex]i) \sqrt{ \frac{169}{256} } = \frac{ \sqrt{169} }{ \sqrt{256} } = \frac{13}{16} [/tex]
[tex]j) \sqrt{ \frac{144}{1225} } = \frac{ \sqrt{144} }{ \sqrt{1225} } = \frac{12}{35} [/tex]
[tex]k) \sqrt{ \frac{196}{324} } ^{(4} = \sqrt{ \frac{49}{81} } = \frac{ \sqrt{49} }{ \sqrt{81} } = \frac{7}{9} [/tex]
[tex]l) \sqrt{ \frac{361}{484} } = \frac{ \sqrt{361} }{ \sqrt{484} } = \frac{19}{22} [/tex]
[tex]6) \\ \\ a) \sqrt{2 \frac{7}{9} } = \sqrt{ \frac{2 \times 9 + 7}{9} } = \sqrt{ \frac{18 + 7}{9} } = \sqrt{ \frac{25}{9} } = \frac{ \sqrt{25} }{ \sqrt{9} } = \frac{5}{3} [/tex]
[tex]b) \sqrt{5 \frac{19}{25} } = \sqrt{ \frac{5 \times 25 + 19}{25} } = \sqrt{ \frac{125 + 19}{25} } = \sqrt{ \frac{144}{25} } = \frac{ \sqrt{144} }{ \sqrt{25} } = \frac{12}{5} = 2 \frac{2}{5} [/tex]
[tex]c) \sqrt{1 \frac{32}{49} } = \sqrt{ \frac{1 \times 49 + 32}{49} } = \sqrt{ \frac{49 + 32}{49} } = \sqrt{ \frac{81}{49} } = \frac{ \sqrt{81} }{ \sqrt{49} } = \frac{9}{7} = 1 \frac{2}{7} [/tex]
[tex]d) \sqrt{11 \frac{1}{9} } = \sqrt{ \frac{11 \times 9 + 1}{9} } = \sqrt{ \frac{99 + 1}{9} } = \sqrt{ \frac{100}{9} } = \frac{ \sqrt{100} }{ \sqrt{9} } = \frac{10}{3} = 3 \frac{1}{3} [/tex]
[tex]e) \sqrt{7 \frac{9}{16} } = \sqrt{ \frac{7 \times 16 + 9}{16} } = \sqrt{ \frac{112 + 9}{16} } = \sqrt{ \frac{121}{16} } = \frac{ \sqrt{121} }{ \sqrt{16} } = \frac{11}{4} = 2 \frac{3}{4} [/tex]
[tex]f) \sqrt{4 \frac{25}{36} } = \sqrt{ \frac{4 \times 36 + 25}{36} } = \sqrt{ \frac{144 + 25}{36} } = \sqrt{ \frac{169}{36} } = \frac{ \sqrt{169} }{ \sqrt{36} } = \frac{13}{6} = 2 \frac{1}{6} [/tex]
[tex]g) \sqrt{4 \frac{33}{64} } = \sqrt{ \frac{4 \times 64 + 33}{64} } = \sqrt{ \frac{256 + 33}{64} } = \sqrt{ \frac{289}{64} } = \frac{ \sqrt{289} }{ \sqrt{164} } = \frac{17}{8} = 2 \frac{1}{8} [/tex]
[tex]h) \sqrt{20 \frac{1}{4} } = \sqrt{ \frac{20 \times 4 + 1}{4} } = \sqrt{ \frac{80 + 1}{4} } = \sqrt{ \frac{81}{4} } = \frac{ \sqrt{81} }{ \sqrt{4} } = \frac{9}{2} = 4 \frac{1}{2} [/tex]
[tex]i) \sqrt{7 \frac{21}{25} } = \sqrt{ \frac{7 \times 25 + 21}{25} } = \sqrt{ \frac{175 + 21}{25} } = \sqrt{ \frac{196}{25} } = \frac{ \sqrt{196} }{ \sqrt{25} } = \frac{14}{5} = 2 \frac{4}{5} [/tex]
[tex]j) \sqrt{6 \frac{30}{49} } = \sqrt{ \frac{6 \times 49 + 30}{49} } = \sqrt{ \frac{294 + 30}{49} } = \sqrt{ \frac{324}{49} } = \frac{ \sqrt{324} }{ \sqrt{49} } = \frac{18}{7} = 2 \frac{4}{7} [/tex]
[tex]b) \sqrt{ \frac{81}{64} } = \frac{ \sqrt{81} }{ \sqrt{64} } = \frac{9}{8} [/tex]
[tex]c) \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]
[tex]d) \sqrt{ \frac{144}{169} } = \frac{ \sqrt{144} }{ \sqrt{169} } = \frac{12}{13} [/tex]
[tex]e) \sqrt{ \frac{100}{289} } = \frac{ \sqrt{100} }{ \sqrt{289} } = \frac{10}{17} [/tex]
[tex]f) \sqrt{ \frac{256}{225} } = \frac{ \sqrt{256} }{ \sqrt{225} } = \frac{16}{15} [/tex]
[tex]g) \sqrt{ \frac{196}{289} } = \frac{ \sqrt{196} }{ \sqrt{289} } = \frac{14}{17} [/tex]
[tex]h) \sqrt{ \frac{625}{324} } = \frac{ \sqrt{625} }{ \sqrt{324} } = \frac{25}{18} [/tex]
[tex]i) \sqrt{ \frac{169}{256} } = \frac{ \sqrt{169} }{ \sqrt{256} } = \frac{13}{16} [/tex]
[tex]j) \sqrt{ \frac{144}{1225} } = \frac{ \sqrt{144} }{ \sqrt{1225} } = \frac{12}{35} [/tex]
[tex]k) \sqrt{ \frac{196}{324} } ^{(4} = \sqrt{ \frac{49}{81} } = \frac{ \sqrt{49} }{ \sqrt{81} } = \frac{7}{9} [/tex]
[tex]l) \sqrt{ \frac{361}{484} } = \frac{ \sqrt{361} }{ \sqrt{484} } = \frac{19}{22} [/tex]
[tex]6) \\ \\ a) \sqrt{2 \frac{7}{9} } = \sqrt{ \frac{2 \times 9 + 7}{9} } = \sqrt{ \frac{18 + 7}{9} } = \sqrt{ \frac{25}{9} } = \frac{ \sqrt{25} }{ \sqrt{9} } = \frac{5}{3} [/tex]
[tex]b) \sqrt{5 \frac{19}{25} } = \sqrt{ \frac{5 \times 25 + 19}{25} } = \sqrt{ \frac{125 + 19}{25} } = \sqrt{ \frac{144}{25} } = \frac{ \sqrt{144} }{ \sqrt{25} } = \frac{12}{5} = 2 \frac{2}{5} [/tex]
[tex]c) \sqrt{1 \frac{32}{49} } = \sqrt{ \frac{1 \times 49 + 32}{49} } = \sqrt{ \frac{49 + 32}{49} } = \sqrt{ \frac{81}{49} } = \frac{ \sqrt{81} }{ \sqrt{49} } = \frac{9}{7} = 1 \frac{2}{7} [/tex]
[tex]d) \sqrt{11 \frac{1}{9} } = \sqrt{ \frac{11 \times 9 + 1}{9} } = \sqrt{ \frac{99 + 1}{9} } = \sqrt{ \frac{100}{9} } = \frac{ \sqrt{100} }{ \sqrt{9} } = \frac{10}{3} = 3 \frac{1}{3} [/tex]
[tex]e) \sqrt{7 \frac{9}{16} } = \sqrt{ \frac{7 \times 16 + 9}{16} } = \sqrt{ \frac{112 + 9}{16} } = \sqrt{ \frac{121}{16} } = \frac{ \sqrt{121} }{ \sqrt{16} } = \frac{11}{4} = 2 \frac{3}{4} [/tex]
[tex]f) \sqrt{4 \frac{25}{36} } = \sqrt{ \frac{4 \times 36 + 25}{36} } = \sqrt{ \frac{144 + 25}{36} } = \sqrt{ \frac{169}{36} } = \frac{ \sqrt{169} }{ \sqrt{36} } = \frac{13}{6} = 2 \frac{1}{6} [/tex]
[tex]g) \sqrt{4 \frac{33}{64} } = \sqrt{ \frac{4 \times 64 + 33}{64} } = \sqrt{ \frac{256 + 33}{64} } = \sqrt{ \frac{289}{64} } = \frac{ \sqrt{289} }{ \sqrt{164} } = \frac{17}{8} = 2 \frac{1}{8} [/tex]
[tex]h) \sqrt{20 \frac{1}{4} } = \sqrt{ \frac{20 \times 4 + 1}{4} } = \sqrt{ \frac{80 + 1}{4} } = \sqrt{ \frac{81}{4} } = \frac{ \sqrt{81} }{ \sqrt{4} } = \frac{9}{2} = 4 \frac{1}{2} [/tex]
[tex]i) \sqrt{7 \frac{21}{25} } = \sqrt{ \frac{7 \times 25 + 21}{25} } = \sqrt{ \frac{175 + 21}{25} } = \sqrt{ \frac{196}{25} } = \frac{ \sqrt{196} }{ \sqrt{25} } = \frac{14}{5} = 2 \frac{4}{5} [/tex]
[tex]j) \sqrt{6 \frac{30}{49} } = \sqrt{ \frac{6 \times 49 + 30}{49} } = \sqrt{ \frac{294 + 30}{49} } = \sqrt{ \frac{324}{49} } = \frac{ \sqrt{324} }{ \sqrt{49} } = \frac{18}{7} = 2 \frac{4}{7} [/tex]
Vă mulțumim că ați ales să vizitați site-ul nostru dedicat Matematică. Sperăm că informațiile prezentate v-au fost utile. Dacă aveți alte întrebări sau aveți nevoie de asistență suplimentară, nu ezitați să ne contactați. Vă așteptăm cu drag să reveniți și nu uitați să ne salvați în lista de favorite!