Resolver 2*250/0.05^2*1.256610^-6frac{8*1.58*154{sqrt{12}5*0.2}}

$$\frac{ 2 \cdot 250 }{ { 0.05 }^{ 2 } \times 1.2566 { 10 }^{ -6 } \frac{ 8 \cdot 1.58 \cdot 154 }{ \sqrt{ 12 } 5 \cdot 0.2 } }$$

Avaliar

$$\frac{6250000000000000\sqrt{3}}{38219489}\approx 283240771.41129446$$

Passos Para a Resolução

Multiplique 2 e 250 para obter 500.

$$\frac{500}{1.2566\times 0.05^{2}\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Calcule 0.05 elevado a 2 e obtenha 0.0025.

$$\frac{500}{1.2566\times 0.0025\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiplique 1.2566 e 0.0025 para obter 0.0031415.

$$\frac{500}{0.0031415\times 10^{-6}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Calcule 10 elevado a -6 e obtenha \frac{1}{1000000}.

$$\frac{500}{0.0031415\times \frac{1}{1000000}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiplique 0.0031415 e \frac{1}{1000000} para obter \frac{6283}{2000000000000}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{8\times 1.58\times 154}{0.2\times 5\sqrt{12}}}$$

Multiplique 8 e 1.58 para obter 12.64.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{12.64\times 154}{0.2\times 5\sqrt{12}}}$$

Multiplique 12.64 e 154 para obter 1946.56.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{0.2\times 5\sqrt{12}}}$$

Multiplique 0.2 e 5 para obter 1.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{\sqrt{12}}}$$

Fatorize a expressão 12=2^{2}\times 3. Reescreva a raiz quadrada do produto \sqrt{2^{2}\times 3} como o produto de raízes quadradas \sqrt{2^{2}}\sqrt{3}. Calcule a raiz quadrada de 2^{2}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56}{2\sqrt{3}}}$$

Racionalize o denominador de \frac{1946.56}{2\sqrt{3}} ao multiplicar o numerador e o denominador por \sqrt{3}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}}$$

O quadrado de \sqrt{3} é 3.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{2\times 3}}$$

Multiplique 2 e 3 para obter 6.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{1946.56\sqrt{3}}{6}}$$

Dividir 1946.56\sqrt{3} por 6 para obter \frac{24332}{75}\sqrt{3}.

$$\frac{500}{\frac{6283}{2000000000000}\times \frac{24332}{75}\sqrt{3}}$$

Multiplique \frac{6283}{2000000000000} e \frac{24332}{75} para obter \frac{38219489}{37500000000000}.

$$\frac{500}{\frac{38219489}{37500000000000}\sqrt{3}}$$

Racionalize o denominador de \frac{500}{\frac{38219489}{37500000000000}\sqrt{3}} ao multiplicar o numerador e o denominador por \sqrt{3}.

$$\frac{500\sqrt{3}}{\frac{38219489}{37500000000000}\left(\sqrt{3}\right)^{2}}$$

O quadrado de \sqrt{3} é 3.

$$\frac{500\sqrt{3}}{\frac{38219489}{37500000000000}\times 3}$$

Multiplique \frac{38219489}{37500000000000} e 3 para obter \frac{38219489}{12500000000000}.

$$\frac{500\sqrt{3}}{\frac{38219489}{12500000000000}}$$

Divida 500\sqrt{3} por \frac{38219489}{12500000000000} ao multiplicar 500\sqrt{3} pelo recíproco de \frac{38219489}{12500000000000}.

$$\frac{500\sqrt{3}\times 12500000000000}{38219489}$$

Multiplique 500 e 12500000000000 para obter 6250000000000000.

$$\frac{6250000000000000\sqrt{3}}{38219489}$$