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

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

Calcular

$$\frac{\sqrt{910}}{22750000000000000000000000}\approx 1.325987088 \cdot 10^{-24}$$

Pasos da solución

Para dividir potencias da mesma base, resta o expoñente do numerador ao expoñente do denominador.

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

Multiplica 2 e 16 para obter 32.

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

Multiplica 32 e 500 para obter 16000.

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

Calcula 10 á potencia de 50 e obtén 100000000000000000000000000000000000000000000000000.

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

Multiplica 91 e 100000000000000000000000000000000000000000000000000 para obter 9100000000000000000000000000000000000000000000000000.

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

Reduce a fracción \frac{16000}{9100000000000000000000000000000000000000000000000000} a termos máis baixos extraendo e cancelando 16000.

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

Reescribe a raíz cadrada da división \sqrt{\frac{1}{568750000000000000000000000000000000000000000000}} como a división de raíces cadradas \frac{\sqrt{1}}{\sqrt{568750000000000000000000000000000000000000000000}}.

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

Calcular a raíz cadrada de 1 e obter 1.

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

Factoriza 568750000000000000000000000000000000000000000000=25000000000000000000000^{2}\times 910. Reescribe a raíz cadrada do produto \sqrt{25000000000000000000000^{2}\times 910} como o produto de raíces cadradas \sqrt{25000000000000000000000^{2}}\sqrt{910}. Obtén a raíz cadrada de 25000000000000000000000^{2}.

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

Racionaliza o denominador de \frac{1}{25000000000000000000000\sqrt{910}} mediante a multiplicación do numerador e o denominador por \sqrt{910}.

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

O cadrado de \sqrt{910} é 910.

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

Multiplica 25000000000000000000000 e 910 para obter 22750000000000000000000000.

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