Răspuns :
3 a. √2^2×3^2= 2×3 =6
√5^4×6^2=√5^2×5^2×6^2=5×5×6=150
și așa se fac toate se aduc la puterea 2 și ies de sub radical
√5^4×6^2=√5^2×5^2×6^2=5×5×6=150
și așa se fac toate se aduc la puterea 2 și ies de sub radical
2. a) [tex] \sqrt{0.04*0.09}= \sqrt{0.0036}= \sqrt{ \frac{9}{2500} } = \frac{3}{50} [/tex];
[tex] \sqrt{1.44*0.01}= \sqrt{0.0144}= \sqrt{ \frac{9}{625} }= \frac{3}{25} [/tex];
[tex] \sqrt{0.36*1.96}= \sqrt{0.7056}= \sqrt{ \frac{441}{625} }= \frac{21}{25} [/tex];
[tex] \sqrt{2.25*16}= \sqrt{36}=6 [/tex];
[tex] \sqrt{3.24*0.0001}= \sqrt{0.000324}= \sqrt{ \frac{81}{250000} }= \frac{9}{500} [/tex];
[tex] \sqrt{0.0324*100}= \sqrt{3.24}= \sqrt{ \frac{81}{25} }= \frac{9}{5} [/tex];
[tex] \sqrt{5.76*9.61}= \sqrt{55.3536}= \sqrt{ \frac{34596}{625} }= \frac{186}{25} [/tex];
b) [tex] \sqrt{ \frac{1.69}{0.25} }= \sqrt{ \frac{169}{ \frac{100}{ \frac{1}{4} } } } = \frac{13}{ \frac{10}{ \frac{1}{2} } } = \frac{13}{5} [/tex];
[tex] \sqrt{ \frac{0.0016}{0.0025} }= \sqrt{ \frac{1}{ \frac{625}{ \frac{1}{400} } } }= \frac{1}{ \frac{25}{ \frac{1}{20} } }= \frac{4}{5} [/tex];
[tex] \sqrt{ \frac{10.89 }{0.04} } = \sqrt{ \frac{1089}{ \frac{100}{ \frac{1}{25} } } } = \frac{33}{ \frac{10}{ \frac{1}{5} } } = \frac{33}{2} [/tex];
[tex] \sqrt{ \frac{12.96}{7.29} }= \sqrt{ \frac{324}{ \frac{25}{ \frac{729}{100} } } } = \frac{18}{ \frac{5}{ \frac{27}{10} } }= \frac{4}{3} [/tex];
[tex] \sqrt{ \frac{0.81}{7.29} }= \sqrt{ \frac{81}{ \frac{100}{ \frac{729}{100} } }} = \frac{9}{ \frac{10}{ \frac{27}{10} } } = \frac{9}{27}= \frac{1}{3} [/tex];
[tex] \sqrt{ \frac{84.64}{21.16} } = \sqrt{ \frac{2116}{ \frac{25}{ \frac{529}{25} } } }= \frac{46}{ \frac{5}{ \frac{23}{5} } } = \frac{46}{23} =2[/tex];
[tex] \sqrt{ \frac{12.96 }{23.04} } = \sqrt{ \frac{324}{ \frac{25}{ \frac{576}{25} } } }= \frac{18}{ \frac{5}{ \frac{24}{5} } } = \frac{18}{24} = \frac{3}{4} [/tex];
[tex] \sqrt{ \frac{65.61}{7.29} }= \sqrt{ \frac{6561}{ \frac{100}{ \frac{729}{100} } } } = \frac{81}{ \frac{10}{ \frac{27}{10} } } = \frac{81}{27}=3 [/tex];
[tex] \sqrt{ \frac{4.41}{5.76} } = \sqrt{ \frac{441}{ \frac{100}{ \frac{144}{100} } } }= \frac{21}{ \frac{10}{ \frac{12}{10} } } = \frac{7}{8} [/tex];
[tex] \sqrt{ \frac{12.25}{1.96} } = \sqrt{ \frac{49}{ \frac{4}{ \frac{49}{25} } } }= \frac{7}{ \frac{2}{ \frac{7}{5} } } = \frac{5}{2} [/tex].
3. a) [tex] \sqrt{ 2^{2}* 3^{2} } =2*3=6[/tex];
[tex]\sqrt{ 5^{4}* 6^{2}}= 5^{2}*6= 25*6=150[/tex];
[tex]\sqrt{ 2^{4}* 5^{2}* 10^{6}} = 2^{2}*5* 10^{3} =4*5* 10^{3}=20* 10^{3}=2*10* 10^{3}[/tex][tex]=2* 10^{4}=2*10000=20000 [/tex];
[tex]\sqrt{ 3^{3}* 2^{5}* 6^{3}}= \sqrt{27*32* 6^{3} }= \sqrt{864* 6^{3} } = \sqrt{4* 6^{3}* 6^{3} }[/tex][tex]=\sqrt{4* 6^{6} } =2* 6^{3}=2*216*432 [/tex];
[tex]\sqrt{ 14* 2^{4}* 7}= \sqrt{14*8*7}= \sqrt{784}=28 [/tex];
[tex]\sqrt{ 9^{3}* 2^{4}* 3^{4}}= \sqrt{( 3^{2}) ^{3}* 2^{4}* 3^{4} } = \sqrt{ 3^{6}*2^{4}* 3^{4} } = 3^{3}* 2^{2}* 3^{2}[/tex][tex]=3^{3}*4 * 3^{2} =4* 3^{5}=4*243=972 [/tex];
[tex]\sqrt{ 125* 5^{3}* 10^{2}* 2^{4} }= \sqrt{ 5^{3}* 5^{3}*100*16 }= \sqrt{ 5^{3}* 5^{3}*4* 5^{2}*16 } [/tex][tex]= \sqrt{64* 5^{8} }=8* 5^{4}=8*625=5000 [/tex];
[tex]\sqrt{ 15^{3}* 5* 3^{3}}= \sqrt{ 15^{3}*5*27}= \sqrt{135* 15^{3} }= \sqrt{9*15* 15^{3}}= \sqrt{9* 15^{4}} [/tex][tex]=3* 15^{2}=3*225=675[/tex];
b) [tex] \sqrt{ \frac{3 ^{2} }{ 5^{4} } }= \frac{3}{ 5^{2} } = \frac{3}{25} [/tex];
[tex] \sqrt{ \frac{4 }{ 6^{4} } }= \frac{2}{ 6^{2} }= \frac{2}{36}= \frac{2}{18} [/tex];
[tex] \sqrt{ \frac{21 ^{2} }{ 14^{4} } }= \frac{21}{14^{4}} = \frac{21}{196}= \frac{3}{28} [/tex];
[tex] \sqrt{ \frac{16 ^{2} }{ 6^{4} } }= \frac{16}{ 6^{2} } = \frac{16}{36}= \frac{4}{9} [/tex];
[tex] \sqrt{ \frac{5 ^{3} }{ 10^{2}*20 } }= \sqrt{ \frac{ 5^{3} }{ 2^{2}* 5^{2}*4*5 } }= \sqrt{ \frac{5}{4*4*5} }= \sqrt{ \frac{1}{4*4} } = \frac{1}{2*2}= \frac{1}{4} [/tex];
[tex]\sqrt{ \frac{15 ^{3}*3 }{ 3^{2}*5 } }= \sqrt{ \frac{5 ^{3}*3 ^{3}}{3*5} }= \sqrt{ 5^{2}* 3^{2} } =5*3=15 [/tex];
[tex]\sqrt{ \frac{36}{ 9^{2}*4 } }= \sqrt{ \frac{9}{9^{2}} }= \sqrt{ \frac{1}{9} }= \frac{1}{3} [/tex];
[tex]\sqrt{ \frac{64*3 ^{3} }{ 3*12 ^{2} } }= \sqrt{ \frac{64*^{3} }{12^{2}} } = \sqrt{ \frac{64}{ 4^{2} } }= \sqrt{ \frac{64}{16} }= \sqrt{4} =2 [/tex];
[tex]\sqrt{ \frac{11{4} }{ 22 ^{2} *33 ^{2} } }= \frac{ 11^{2} }{22*33}= \frac{ 11^{2} }{2*11*3*11}= \frac{11}{2*3*11} = \frac{1}{2*3} = \frac{1}{6} [/tex];
[tex] \sqrt{1.44*0.01}= \sqrt{0.0144}= \sqrt{ \frac{9}{625} }= \frac{3}{25} [/tex];
[tex] \sqrt{0.36*1.96}= \sqrt{0.7056}= \sqrt{ \frac{441}{625} }= \frac{21}{25} [/tex];
[tex] \sqrt{2.25*16}= \sqrt{36}=6 [/tex];
[tex] \sqrt{3.24*0.0001}= \sqrt{0.000324}= \sqrt{ \frac{81}{250000} }= \frac{9}{500} [/tex];
[tex] \sqrt{0.0324*100}= \sqrt{3.24}= \sqrt{ \frac{81}{25} }= \frac{9}{5} [/tex];
[tex] \sqrt{5.76*9.61}= \sqrt{55.3536}= \sqrt{ \frac{34596}{625} }= \frac{186}{25} [/tex];
b) [tex] \sqrt{ \frac{1.69}{0.25} }= \sqrt{ \frac{169}{ \frac{100}{ \frac{1}{4} } } } = \frac{13}{ \frac{10}{ \frac{1}{2} } } = \frac{13}{5} [/tex];
[tex] \sqrt{ \frac{0.0016}{0.0025} }= \sqrt{ \frac{1}{ \frac{625}{ \frac{1}{400} } } }= \frac{1}{ \frac{25}{ \frac{1}{20} } }= \frac{4}{5} [/tex];
[tex] \sqrt{ \frac{10.89 }{0.04} } = \sqrt{ \frac{1089}{ \frac{100}{ \frac{1}{25} } } } = \frac{33}{ \frac{10}{ \frac{1}{5} } } = \frac{33}{2} [/tex];
[tex] \sqrt{ \frac{12.96}{7.29} }= \sqrt{ \frac{324}{ \frac{25}{ \frac{729}{100} } } } = \frac{18}{ \frac{5}{ \frac{27}{10} } }= \frac{4}{3} [/tex];
[tex] \sqrt{ \frac{0.81}{7.29} }= \sqrt{ \frac{81}{ \frac{100}{ \frac{729}{100} } }} = \frac{9}{ \frac{10}{ \frac{27}{10} } } = \frac{9}{27}= \frac{1}{3} [/tex];
[tex] \sqrt{ \frac{84.64}{21.16} } = \sqrt{ \frac{2116}{ \frac{25}{ \frac{529}{25} } } }= \frac{46}{ \frac{5}{ \frac{23}{5} } } = \frac{46}{23} =2[/tex];
[tex] \sqrt{ \frac{12.96 }{23.04} } = \sqrt{ \frac{324}{ \frac{25}{ \frac{576}{25} } } }= \frac{18}{ \frac{5}{ \frac{24}{5} } } = \frac{18}{24} = \frac{3}{4} [/tex];
[tex] \sqrt{ \frac{65.61}{7.29} }= \sqrt{ \frac{6561}{ \frac{100}{ \frac{729}{100} } } } = \frac{81}{ \frac{10}{ \frac{27}{10} } } = \frac{81}{27}=3 [/tex];
[tex] \sqrt{ \frac{4.41}{5.76} } = \sqrt{ \frac{441}{ \frac{100}{ \frac{144}{100} } } }= \frac{21}{ \frac{10}{ \frac{12}{10} } } = \frac{7}{8} [/tex];
[tex] \sqrt{ \frac{12.25}{1.96} } = \sqrt{ \frac{49}{ \frac{4}{ \frac{49}{25} } } }= \frac{7}{ \frac{2}{ \frac{7}{5} } } = \frac{5}{2} [/tex].
3. a) [tex] \sqrt{ 2^{2}* 3^{2} } =2*3=6[/tex];
[tex]\sqrt{ 5^{4}* 6^{2}}= 5^{2}*6= 25*6=150[/tex];
[tex]\sqrt{ 2^{4}* 5^{2}* 10^{6}} = 2^{2}*5* 10^{3} =4*5* 10^{3}=20* 10^{3}=2*10* 10^{3}[/tex][tex]=2* 10^{4}=2*10000=20000 [/tex];
[tex]\sqrt{ 3^{3}* 2^{5}* 6^{3}}= \sqrt{27*32* 6^{3} }= \sqrt{864* 6^{3} } = \sqrt{4* 6^{3}* 6^{3} }[/tex][tex]=\sqrt{4* 6^{6} } =2* 6^{3}=2*216*432 [/tex];
[tex]\sqrt{ 14* 2^{4}* 7}= \sqrt{14*8*7}= \sqrt{784}=28 [/tex];
[tex]\sqrt{ 9^{3}* 2^{4}* 3^{4}}= \sqrt{( 3^{2}) ^{3}* 2^{4}* 3^{4} } = \sqrt{ 3^{6}*2^{4}* 3^{4} } = 3^{3}* 2^{2}* 3^{2}[/tex][tex]=3^{3}*4 * 3^{2} =4* 3^{5}=4*243=972 [/tex];
[tex]\sqrt{ 125* 5^{3}* 10^{2}* 2^{4} }= \sqrt{ 5^{3}* 5^{3}*100*16 }= \sqrt{ 5^{3}* 5^{3}*4* 5^{2}*16 } [/tex][tex]= \sqrt{64* 5^{8} }=8* 5^{4}=8*625=5000 [/tex];
[tex]\sqrt{ 15^{3}* 5* 3^{3}}= \sqrt{ 15^{3}*5*27}= \sqrt{135* 15^{3} }= \sqrt{9*15* 15^{3}}= \sqrt{9* 15^{4}} [/tex][tex]=3* 15^{2}=3*225=675[/tex];
b) [tex] \sqrt{ \frac{3 ^{2} }{ 5^{4} } }= \frac{3}{ 5^{2} } = \frac{3}{25} [/tex];
[tex] \sqrt{ \frac{4 }{ 6^{4} } }= \frac{2}{ 6^{2} }= \frac{2}{36}= \frac{2}{18} [/tex];
[tex] \sqrt{ \frac{21 ^{2} }{ 14^{4} } }= \frac{21}{14^{4}} = \frac{21}{196}= \frac{3}{28} [/tex];
[tex] \sqrt{ \frac{16 ^{2} }{ 6^{4} } }= \frac{16}{ 6^{2} } = \frac{16}{36}= \frac{4}{9} [/tex];
[tex] \sqrt{ \frac{5 ^{3} }{ 10^{2}*20 } }= \sqrt{ \frac{ 5^{3} }{ 2^{2}* 5^{2}*4*5 } }= \sqrt{ \frac{5}{4*4*5} }= \sqrt{ \frac{1}{4*4} } = \frac{1}{2*2}= \frac{1}{4} [/tex];
[tex]\sqrt{ \frac{15 ^{3}*3 }{ 3^{2}*5 } }= \sqrt{ \frac{5 ^{3}*3 ^{3}}{3*5} }= \sqrt{ 5^{2}* 3^{2} } =5*3=15 [/tex];
[tex]\sqrt{ \frac{36}{ 9^{2}*4 } }= \sqrt{ \frac{9}{9^{2}} }= \sqrt{ \frac{1}{9} }= \frac{1}{3} [/tex];
[tex]\sqrt{ \frac{64*3 ^{3} }{ 3*12 ^{2} } }= \sqrt{ \frac{64*^{3} }{12^{2}} } = \sqrt{ \frac{64}{ 4^{2} } }= \sqrt{ \frac{64}{16} }= \sqrt{4} =2 [/tex];
[tex]\sqrt{ \frac{11{4} }{ 22 ^{2} *33 ^{2} } }= \frac{ 11^{2} }{22*33}= \frac{ 11^{2} }{2*11*3*11}= \frac{11}{2*3*11} = \frac{1}{2*3} = \frac{1}{6} [/tex];
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