Resolver -{[(1/sqrt{4})-(-1/sqrt{9})]+(-sqrt{4})^3+2(sqrt{16}-1/2)}div(3/4)

$$- \{ [ ( \frac { 1 } { \sqrt { 4 } } ) - ( - \frac { 1 } { \sqrt { 9 } } ) ] + ( - \sqrt { 4 } ) ^ { 3 } + 2 ( \sqrt { 16 } - \frac { 1 } { 2 } ) \} \div ( \frac { 3 } { 4 } )$$

Avaliar

$$\frac{2}{9}\approx 0,222222222$$

Passos Para a Resolução

Calcule a raiz quadrada de 4 e obtenha 2.

$$\frac{-\left(\frac{1}{2}-\left(-\frac{1}{\sqrt{9}}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calcule a raiz quadrada de 9 e obtenha 3.

$$\frac{-\left(\frac{1}{2}-\left(-\frac{1}{3}\right)+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

O oposto de -\frac{1}{3} é \frac{1}{3}.

$$\frac{-\left(\frac{1}{2}+\frac{1}{3}+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Some \frac{1}{2} e \frac{1}{3} para obter \frac{5}{6}.

$$\frac{-\left(\frac{5}{6}+\left(-\sqrt{4}\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calcule a raiz quadrada de 4 e obtenha 2.

$$\frac{-\left(\frac{5}{6}+\left(-2\right)^{3}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calcule -2 elevado a 3 e obtenha -8.

$$\frac{-\left(\frac{5}{6}-8+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Subtraia 8 de \frac{5}{6} para obter -\frac{43}{6}.

$$\frac{-\left(-\frac{43}{6}+2\left(\sqrt{16}-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Calcule a raiz quadrada de 16 e obtenha 4.

$$\frac{-\left(-\frac{43}{6}+2\left(4-\frac{1}{2}\right)\right)}{\frac{3}{4}}$$

Subtraia \frac{1}{2} de 4 para obter \frac{7}{2}.

$$\frac{-\left(-\frac{43}{6}+2\times \frac{7}{2}\right)}{\frac{3}{4}}$$

Multiplique 2 e \frac{7}{2} para obter 7.

$$\frac{-\left(-\frac{43}{6}+7\right)}{\frac{3}{4}}$$

Some -\frac{43}{6} e 7 para obter -\frac{1}{6}.

$$\frac{-\left(-\frac{1}{6}\right)}{\frac{3}{4}}$$

O oposto de -\frac{1}{6} é \frac{1}{6}.

$$\frac{\frac{1}{6}}{\frac{3}{4}}$$

Divida \frac{1}{6} por \frac{3}{4} ao multiplicar \frac{1}{6} pelo recíproco de \frac{3}{4}.

$$\frac{1}{6}\times \frac{4}{3}$$

Multiplique \frac{1}{6} e \frac{4}{3} para obter \frac{2}{9}.

$$\frac{2}{9}$$

Fatorizar

$$\frac{2}{3 ^ {2}} = 0,2222222222222222$$