Resolver sqrt{(11/4*8/11)^2:[(23/12-3/2):frac{5}{4}]^2}-sqrt{10+[(frac{1}{2})^2:frac{1}{2}+frac{12}{13}*(frac{5}{4}-frac{1}{6})]:frac{8}{3}}

$$\sqrt { ( \frac { 11 } { 4 } \times \frac { 8 } { 11 } ) ^ { 2 } : [ ( \frac { 23 } { 12 } - \frac { 3 } { 2 } ) : \frac { 5 } { 4 } ] ^ { 2 } } - \sqrt { 10 + [ ( \frac { 1 } { 2 } ) ^ { 2 } : \frac { 1 } { 2 } + \frac { 12 } { 13 } \times ( \frac { 5 } { 4 } - \frac { 1 } { 6 } ) ] : \frac { 8 } { 3 } }$$

Avaliar

$$\frac{11}{4}=2,75$$

Passos Para a Resolução

Para dividir as potências da mesma base, subtraia o expoente do denominador do expoente do numerador. Subtraia 1 de 2 para obter 1.

$$\sqrt{\frac{\left(\frac{11}{4}\times \frac{8}{11}\right)^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplique \frac{11}{4} e \frac{8}{11} para obter 2.

$$\sqrt{\frac{2^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcule 2 elevado a 2 e obtenha 4.

$$\sqrt{\frac{4}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Subtraia \frac{3}{2} de \frac{23}{12} para obter \frac{5}{12}.

$$\sqrt{\frac{4}{\left(\frac{\frac{5}{12}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Divida \frac{5}{12} por \frac{5}{4} ao multiplicar \frac{5}{12} pelo recíproco de \frac{5}{4}.

$$\sqrt{\frac{4}{\left(\frac{5}{12}\times \frac{4}{5}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplique \frac{5}{12} e \frac{4}{5} para obter \frac{1}{3}.

$$\sqrt{\frac{4}{\left(\frac{1}{3}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcule \frac{1}{3} elevado a 2 e obtenha \frac{1}{9}.

$$\sqrt{\frac{4}{\frac{1}{9}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Divida 4 por \frac{1}{9} ao multiplicar 4 pelo recíproco de \frac{1}{9}.

$$\sqrt{4\times 9}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplique 4 e 9 para obter 36.

$$\sqrt{36}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcule a raiz quadrada de 36 e obtenha 6.

$$6-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcule \frac{1}{2} elevado a 1 e obtenha \frac{1}{2}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Subtraia \frac{1}{6} de \frac{5}{4} para obter \frac{13}{12}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\times \frac{13}{12}}{\frac{8}{3}}}$$

Multiplique \frac{12}{13} e \frac{13}{12} para obter 1.

$$6-\sqrt{10+\frac{\frac{1}{2}+1}{\frac{8}{3}}}$$

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

$$6-\sqrt{10+\frac{\frac{3}{2}}{\frac{8}{3}}}$$

Divida \frac{3}{2} por \frac{8}{3} ao multiplicar \frac{3}{2} pelo recíproco de \frac{8}{3}.

$$6-\sqrt{10+\frac{3}{2}\times \frac{3}{8}}$$

Multiplique \frac{3}{2} e \frac{3}{8} para obter \frac{9}{16}.

$$6-\sqrt{10+\frac{9}{16}}$$

Some 10 e \frac{9}{16} para obter \frac{169}{16}.

$$6-\sqrt{\frac{169}{16}}$$

Reescreva a raiz quadrada da divisão \frac{169}{16} à medida que a divisão de raízes quadradas \frac{\sqrt{169}}{\sqrt{16}}. Calcule a raiz quadrada do numerador e do denominador.

$$6-\frac{13}{4}$$

Subtraia \frac{13}{4} de 6 para obter \frac{11}{4}.

$$\frac{11}{4}$$

Fatorizar

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2,75$$