Resolver sqrt{(3.7*10^-9)(5.0*10^-10)^2/(8.99*10^9)}

$$\sqrt { \frac { ( 3.7 \times 10 ^ { - 9 } ) ( 5.0 \times 10 ^ { - 10 } ) ^ { 2 } } { ( 8.99 \times 10 ^ { 9 } ) } }$$

Calcular

$$\frac{\sqrt{332630}}{1798000000000000000000}\approx 3.207679883 \cdot 10^{-19}$$

Pasos da solución

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

$$\sqrt{\frac{3.7\times \left(5\times 10^{-10}\right)^{2}}{8.99\times 10^{18}}}$$

Calcula 10 á potencia de -10 e obtén \frac{1}{10000000000}.

$$\sqrt{\frac{3.7\times \left(5\times \frac{1}{10000000000}\right)^{2}}{8.99\times 10^{18}}}$$

Multiplica 5 e \frac{1}{10000000000} para obter \frac{1}{2000000000}.

$$\sqrt{\frac{3.7\times \left(\frac{1}{2000000000}\right)^{2}}{8.99\times 10^{18}}}$$

Calcula \frac{1}{2000000000} á potencia de 2 e obtén \frac{1}{4000000000000000000}.

$$\sqrt{\frac{3.7\times \frac{1}{4000000000000000000}}{8.99\times 10^{18}}}$$

Multiplica 3.7 e \frac{1}{4000000000000000000} para obter \frac{37}{40000000000000000000}.

$$\sqrt{\frac{\frac{37}{40000000000000000000}}{8.99\times 10^{18}}}$$

Calcula 10 á potencia de 18 e obtén 1000000000000000000.

$$\sqrt{\frac{\frac{37}{40000000000000000000}}{8.99\times 1000000000000000000}}$$

Multiplica 8.99 e 1000000000000000000 para obter 8990000000000000000.

$$\sqrt{\frac{\frac{37}{40000000000000000000}}{8990000000000000000}}$$

Expresa \frac{\frac{37}{40000000000000000000}}{8990000000000000000} como unha única fracción.

$$\sqrt{\frac{37}{40000000000000000000\times 8990000000000000000}}$$

Multiplica 40000000000000000000 e 8990000000000000000 para obter 359600000000000000000000000000000000000.

$$\sqrt{\frac{37}{359600000000000000000000000000000000000}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{37}{359600000000000000000000000000000000000}} como a división de raíces cadradas \frac{\sqrt{37}}{\sqrt{359600000000000000000000000000000000000}}.

$$\frac{\sqrt{37}}{\sqrt{359600000000000000000000000000000000000}}$$

Factoriza 359600000000000000000000000000000000000=200000000000000000^{2}\times 8990. Reescribe a raíz cadrada do produto \sqrt{200000000000000000^{2}\times 8990} como o produto de raíces cadradas \sqrt{200000000000000000^{2}}\sqrt{8990}. Obtén a raíz cadrada de 200000000000000000^{2}.

$$\frac{\sqrt{37}}{200000000000000000\sqrt{8990}}$$

Racionaliza o denominador de \frac{\sqrt{37}}{200000000000000000\sqrt{8990}} mediante a multiplicación do numerador e o denominador por \sqrt{8990}.

$$\frac{\sqrt{37}\sqrt{8990}}{200000000000000000\left(\sqrt{8990}\right)^{2}}$$

O cadrado de \sqrt{8990} é 8990.

$$\frac{\sqrt{37}\sqrt{8990}}{200000000000000000\times 8990}$$

Para multiplicar \sqrt{37} e \sqrt{8990}, multiplica os números baixo a raíz cadrada.

$$\frac{\sqrt{332630}}{200000000000000000\times 8990}$$

Multiplica 200000000000000000 e 8990 para obter 1798000000000000000000.

$$\frac{\sqrt{332630}}{1798000000000000000000}$$