Resposta :
Resposta:
a) [tex](3+\sqrt{2} )\sqrt{19}[/tex]
b) [tex]2\sqrt{x30}[/tex]
c) [tex]15\sqrt{x7}[/tex]
d) [tex]2\sqrt{35}[/tex]
e) 0
f) [tex]13\sqrt{5}[/tex]
Explicação passo-a-passo:
Enunciado e Resolução:
Simplifique as expressões com radicais:
a )
[tex]\sqrt{76} +\sqrt{19} -\sqrt{38} =\sqrt{4*19} +\sqrt{19} +\sqrt{2*19} =\sqrt{4} *\sqrt{19} +\sqrt{19} +\sqrt{2} *\sqrt{19}[/tex]
[tex]= 2\sqrt{19} +1*\sqrt{19} +\sqrt{2} *\sqrt{19} =(2+1+\sqrt{2} )\sqrt{19} =(3+\sqrt{2} )\sqrt{19}[/tex]
b) [tex]\sqrt{240}:\sqrt{2} =\sqrt{240:2} =\sqrt{120} =\sqrt{2*2*2*5*3} =\sqrt{4} *\sqrt{30} =2\sqrt{30}[/tex]
c) [tex]\sqrt{343} +8\sqrt{7} =\sqrt{49*7} +8\sqrt{7} =\sqrt{49}*\sqrt{7} +8\sqrt{7} =7\sqrt{7}+8\sqrt{7}=15\sqrt{7}[/tex]
d) [tex]\sqrt{420} :\sqrt{3} =\sqrt{420:3} =\sqrt{140}=\sqrt{2*2*35} =\sqrt{4} *\sqrt{35} =2\sqrt{35}[/tex]
e) [tex]\sqrt{40} +\sqrt{90} -\sqrt{250} =\sqrt{4*10} +\sqrt{9*10} -\sqrt{25*10} =[/tex]
[tex]=\sqrt{4} *\sqrt{10} +\sqrt{9} *\sqrt{10} -\sqrt{25}*\sqrt{10}=2\sqrt{10} +3\sqrt{10} -5\sqrt{10}[/tex]
[tex]=(2+3-5)\sqrt{10} =0*\sqrt{10} =0[/tex]
f ) [tex]\sqrt{5} +\sqrt{125} +7\sqrt{5} = \sqrt{5} +\sqrt{25*5} +7\sqrt{5}=\sqrt{5} +\sqrt{25} *\sqrt{5} +7\sqrt{5}[/tex]
[tex]=\sqrt{5} +5\sqrt{5} +7\sqrt{5} =(1+5+7)\sqrt{5} =13\sqrt{5}[/tex]
Bom estudo.
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Sinais: ( * ) multiplicação ( : ) divisão