Question

sabendo que (raiz quadrada de 5) é aproximadamente igual a 2,24, calcule o valor aproximado de cada expressao: a)125 b)20 c)500 d)$\frac{1}{5}$ e)605 f)$\frac{45}{4}$ g)80

Answer 1

Resposta:a)~~ \sqrt{125} = \sqrt{5^2.5} =5 \sqrt{5} =5(2,24)=11,20 \\  \\ b)~~ \sqrt{20} = \sqrt{2^2.5} =2 \sqrt{5} =2.(2,24)=4,8 \\  \\ c) ~~\sqrt{500} = \sqrt{2^2.5^2.5} =2.5 \sqrt{5} =10 \sqrt{5} =10,(2,24)=22,4 \\  \\ d)~~ \frac{ \sqrt{1} }{ \sqrt{5} } = \frac{1}{ \sqrt{5} } = \frac{1}{2,24} =0,45 \\  \\ e)~~ \sqrt{605} = \sqrt{5.11^2} =11 \sqrt{5} =11.(2,24)=24,64  

f)~~ \frac{ \sqrt{45} }{ \sqrt{4} } = \frac{ \sqrt{3^2.5} }{2} = \frac{3}{2}  \sqrt{5} = \frac{3.(2,24)}{2} = \frac{6,72}{2} =3,36 \\  \\ g)~~ \frac{ \sqrt{80} }{ \sqrt{81} } = \frac{ \sqrt{2^2.2^2.5} }{9} = \frac{4 \sqrt{5} }{9} = \frac{4.(2,24)}{9} = \frac{8,96}{9}  \\  \\ h)~~ \frac{ \sqrt{720} }{ \sqrt{441} } = \frac{ \sqrt{2^2.2^2.3^2.5} }{ \sqrt{3^2.7^2} } = \frac{2.2.3 \sqrt{5} }{3.7} = \frac{12 \sqrt{5} }{21} = \frac{4 \sqrt{5} }{7} = \frac{4(2,24)}{7} = \frac{8,94}{7} =1,28

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