Resolver sqrt{2*16*10^-19*500/91*10^31}

$$\sqrt{ \frac{ 2 \times 16 \times { 10 }^{ -19 } \times 500 }{ 91 \times { 10 }^{ 31 } } }$$

Avaliar

$$\frac{\sqrt{910}}{22750000000000000000000000}\approx 1,325987088 \cdot 10^{-24}$$

Passos Para a Resolução

Para dividir as potências da mesma base, subtraia o exponente do numerador do exponente do denominador.

$$\sqrt{\frac{2\times 16\times 500}{91\times 10^{50}}}$$

Multiplique 2 e 16 para obter 32.

$$\sqrt{\frac{32\times 500}{91\times 10^{50}}}$$

Multiplique 32 e 500 para obter 16000.

$$\sqrt{\frac{16000}{91\times 10^{50}}}$$

Calcule 10 elevado a 50 e obtenha 100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{91\times 100000000000000000000000000000000000000000000000000}}$$

Multiplique 91 e 100000000000000000000000000000000000000000000000000 para obter 9100000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{16000}{9100000000000000000000000000000000000000000000000000}}$$

Reduza a fração \frac{16000}{9100000000000000000000000000000000000000000000000000} para os termos mais baixos ao retirar e anular 16000.

$$\sqrt{\frac{1}{568750000000000000000000000000000000000000000000}}$$

Reescreva a raiz quadrada da divisão \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} à medida que a divisão de raízes quadradas \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

$$\frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}$$

Calcule a raiz quadrada de 1 e obtenha 1.

$$\frac{1}{\sqrt{568750000000000000000000000000000000000000000000}}$$

Fatorize a expressão 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. Reescreva a raiz quadrada do produto \sqrt{25000000000000000000000^{2}\times 910} à medida que o produto das raízes quadradas \sqrt{25000000000000000000000^{2}}\sqrt{910}. Calcule a raiz quadrada de 25000000000000000000000^{2}.

$$\frac{1}{25000000000000000000000\sqrt{910}}$$

Racionalize o denominador de \frac{1}{25000000000000000000000\sqrt{910}} ao multiplicar o numerador e o denominador por \sqrt{910}.

$$\frac{\sqrt{910}}{25000000000000000000000\left(\sqrt{910}\right)^{2}}$$

O quadrado de \sqrt{910} é 910.

$$\frac{\sqrt{910}}{25000000000000000000000\times 910}$$

Multiplique 25000000000000000000000 e 910 para obter 22750000000000000000000000.

$$\frac{\sqrt{910}}{22750000000000000000000000}$$