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

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

Avaliar

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

Passos Para a Resolução

Calcule 10 elevado a 16 e obtenha 10000000000000000.

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

Multiplique 9 e 10000000000000000 para obter 90000000000000000.

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

Reduza a fração \frac{100}{90000000000000000} para os termos mais baixos ao retirar e anular 100.

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

Converta 1 na fração \frac{900000000000000}{900000000000000}.

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

Uma vez que \frac{900000000000000}{900000000000000} e \frac{1}{900000000000000} têm o mesmo denominador, subtraia-os ao subtrair os respetivos numeradores.

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

Subtraia 1 de 900000000000000 para obter 899999999999999.

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

Reescreva a raiz quadrada da divisão \sqrt{\frac{899999999999999}{900000000000000}} à medida que a divisão de raízes quadradas \frac{\sqrt{899999999999999}}{\sqrt{900000000000000}}.

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

Calcule a raiz quadrada de 900000000000000 e obtenha 30000000.

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

Divida 12 por \frac{\sqrt{899999999999999}}{30000000} ao multiplicar 12 pelo recíproco de \frac{\sqrt{899999999999999}}{30000000}.

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

Racionalize o denominador de \frac{12\times 30000000}{\sqrt{899999999999999}} ao multiplicar o numerador e o denominador por \sqrt{899999999999999}.

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

O quadrado de \sqrt{899999999999999} é 899999999999999.

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

Multiplique 12 e 30000000 para obter 360000000.

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