Resolver 12/sqrt{1-frac{100{910^16}}}

$$\frac{ 12 }{ \sqrt{ 1- \frac{ 100 }{ 9 { 10 }^{ 16 } } } }$$

Calcular

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}\approx 12$$

Pasos da solución

Calcula 10 á potencia de 16 e obtén 10000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{9\times 10000000000000000}}}$$

Multiplica 9 e 10000000000000000 para obter 90000000000000000.

$$\frac{12}{\sqrt{1-\frac{100}{90000000000000000}}}$$

Reduce a fracción \frac{100}{90000000000000000} a termos máis baixos extraendo e cancelando 100.

$$\frac{12}{\sqrt{1-\frac{1}{900000000000000}}}$$

Converter 1 á fracción \frac{900000000000000}{900000000000000}.

$$\frac{12}{\sqrt{\frac{900000000000000}{900000000000000}-\frac{1}{900000000000000}}}$$

Dado que \frac{900000000000000}{900000000000000} e \frac{1}{900000000000000} teñen o mesmo denominador, réstaos mediante a resta dos seus numeradores.

$$\frac{12}{\sqrt{\frac{900000000000000-1}{900000000000000}}}$$

Resta 1 de 900000000000000 para obter 899999999999999.

$$\frac{12}{\sqrt{\frac{899999999999999}{900000000000000}}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{899999999999999}{900000000000000}} como a división de raíces cadradas \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

$$\frac{12}{\frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}}$$

Calcular a raíz cadrada de 900000000000000 e obter 30000000.

$$\frac{12}{\frac{\sqrt{899999999999999}}{30000000}}$$

Divide 12 entre \frac{\sqrt{899999999999999}}{30000000} mediante a multiplicación de 12 polo recíproco de \frac{\sqrt{899999999999999}}{30000000}.

$$\frac{12\times 30000000}{\sqrt{899999999999999}}$$

Racionaliza o denominador de \frac{12\times 30000000}{\sqrt{899999999999999}} mediante a multiplicación do numerador e o denominador por \sqrt{899999999999999}.

$$\frac{12\times 30000000\sqrt{899999999999999}}{\left(\sqrt{899999999999999}\right)^{2}}$$

O cadrado de \sqrt{899999999999999} é 899999999999999.

$$\frac{12\times 30000000\sqrt{899999999999999}}{899999999999999}$$

Multiplica 12 e 30000000 para obter 360000000.

$$\frac{360000000\sqrt{899999999999999}}{899999999999999}$$