Question

gente por favor me ajudem.
√76 + √19 - √38
√240/√2
√343 + 8√7
√420/√3
√40 + √90 - √250
√5 + √125 + 7√5

Answer 1

Resposta:

a) $(3+\sqrt{2} )\sqrt{19}$

b) $2\sqrt{x30}$

c) $15\sqrt{x7}$

d) $2\sqrt{35}$  

e) 0        

f)  $13\sqrt{5}$    

Explicação passo-a-passo:

Enunciado e Resolução:  

Simplifique as expressões com radicais:

a )

$\sqrt{76} +\sqrt{19} -\sqrt{38} =\sqrt{4*19} +\sqrt{19} +\sqrt{2*19} =\sqrt{4} *\sqrt{19} +\sqrt{19} +\sqrt{2} *\sqrt{19}$

$= 2\sqrt{19} +1*\sqrt{19} +\sqrt{2} *\sqrt{19} =(2+1+\sqrt{2} )\sqrt{19} =(3+\sqrt{2} )\sqrt{19}$

b) $\sqrt{240}:\sqrt{2} =\sqrt{240:2} =\sqrt{120} =\sqrt{2*2*2*5*3} =\sqrt{4} *\sqrt{30} =2\sqrt{30}$

c) $\sqrt{343} +8\sqrt{7} =\sqrt{49*7} +8\sqrt{7} =\sqrt{49}*\sqrt{7} +8\sqrt{7} =7\sqrt{7}+8\sqrt{7}=15\sqrt{7}$

d) $\sqrt{420} :\sqrt{3} =\sqrt{420:3} =\sqrt{140}=\sqrt{2*2*35} =\sqrt{4} *\sqrt{35} =2\sqrt{35}$      

e) $\sqrt{40} +\sqrt{90} -\sqrt{250} =\sqrt{4*10} +\sqrt{9*10} -\sqrt{25*10} =$

$=\sqrt{4} *\sqrt{10} +\sqrt{9} *\sqrt{10} -\sqrt{25}*\sqrt{10}=2\sqrt{10} +3\sqrt{10} -5\sqrt{10}$

$=(2+3-5)\sqrt{10} =0*\sqrt{10} =0$  

f )  $\sqrt{5} +\sqrt{125} +7\sqrt{5} = \sqrt{5} +\sqrt{25*5} +7\sqrt{5}=\sqrt{5} +\sqrt{25} *\sqrt{5} +7\sqrt{5}$

     $=\sqrt{5} +5\sqrt{5} +7\sqrt{5} =(1+5+7)\sqrt{5} =13\sqrt{5}$  

Bom estudo.

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Sinais: ( * ) multiplicação  ( : ) divisão