Resolver sqrt{292114*10^36/296*10^-19}

$$\sqrt{ \frac{ 292114 \times { 10 }^{ 36 } }{ 296 \times { 10 }^{ -19 } } }$$

Avaliar

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}\approx 9,934141239 \cdot 10^{28}$$

Passos Para a Resolução

Anule 2 no numerador e no denominador.

$$\sqrt{\frac{146057\times 10^{36}}{148\times 10^{-19}}}$$

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

$$\sqrt{\frac{146057\times 10^{55}}{148}}$$

Calcule 10 elevado a 55 e obtenha 10000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{146057\times 10000000000000000000000000000000000000000000000000000000}{148}}$$

Multiplique 146057 e 10000000000000000000000000000000000000000000000000000000 para obter 1460570000000000000000000000000000000000000000000000000000000.

$$\sqrt{\frac{1460570000000000000000000000000000000000000000000000000000000}{148}}$$

Reduza a fração \frac{1460570000000000000000000000000000000000000000000000000000000}{148} para os termos mais baixos ao retirar e anular 4.

$$\sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}}$$

Reescreva a raiz quadrada da divisão \sqrt{\frac{365142500000000000000000000000000000000000000000000000000000}{37}} à medida que a divisão de raízes quadradas \frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}.

$$\frac{\sqrt{365142500000000000000000000000000000000000000000000000000000}}{\sqrt{37}}$$

Fatorize a expressão 365142500000000000000000000000000000000000000000000000000000=500000000000000000000000000^{2}\times 1460570. Reescreva a raiz quadrada do produto \sqrt{500000000000000000000000000^{2}\times 1460570} à medida que o produto das raízes quadradas \sqrt{500000000000000000000000000^{2}}\sqrt{1460570}. Calcule a raiz quadrada de 500000000000000000000000000^{2}.

$$\frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}}$$

Racionalize o denominador de \frac{500000000000000000000000000\sqrt{1460570}}{\sqrt{37}} ao multiplicar o numerador e o denominador por \sqrt{37}.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{\left(\sqrt{37}\right)^{2}}$$

O quadrado de \sqrt{37} é 37.

$$\frac{500000000000000000000000000\sqrt{1460570}\sqrt{37}}{37}$$

Para multiplicar \sqrt{1460570} e \sqrt{37}, multiplique os números sob a raiz quadrada.

$$\frac{500000000000000000000000000\sqrt{54041090}}{37}$$