Solve (frac{4sqrt{2}}{3})^2+4-sqrt{2}*frac{4sqrt{2}}{3}

$$( \frac { 4 \sqrt { 2 } } { 3 } ) ^ { 2 } + 4 - \sqrt { 2 } \times \frac { 4 \sqrt { 2 } } { 3 }$$

Evaluate

$$\frac{44}{9}\approx 4.888888889$$

Solution Steps

To raise \frac{4\sqrt{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{3^{2}}{3^{2}}.

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

Since \frac{\left(4\sqrt{2}\right)^{2}}{3^{2}} and \frac{4\times 3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

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

Express \sqrt{2}\times \frac{4\sqrt{2}}{3} as a single fraction.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 4 to get 8.

$$\frac{\left(4\sqrt{2}\right)^{2}+4\times 3^{2}}{3^{2}}-\frac{8}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3^{2} and 3 is 9. Multiply \frac{8}{3} times \frac{3}{3}.

$$\frac{\left(4\sqrt{2}\right)^{2}+4\times 3^{2}}{9}-\frac{8\times 3}{9}$$

Since \frac{\left(4\sqrt{2}\right)^{2}+4\times 3^{2}}{9} and \frac{8\times 3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4\sqrt{2}\right)^{2}+4\times 3^{2}-8\times 3}{9}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$\frac{4^{2}\left(\sqrt{2}\right)^{2}+4\times 3^{2}}{3^{2}}-\frac{8}{3}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16\left(\sqrt{2}\right)^{2}+4\times 3^{2}}{3^{2}}-\frac{8}{3}$$

The square of \sqrt{2} is 2.

$$\frac{16\times 2+4\times 3^{2}}{3^{2}}-\frac{8}{3}$$

Multiply 16 and 2 to get 32.

$$\frac{32+4\times 3^{2}}{3^{2}}-\frac{8}{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{32+4\times 9}{3^{2}}-\frac{8}{3}$$

Multiply 4 and 9 to get 36.

$$\frac{32+36}{3^{2}}-\frac{8}{3}$$

Add 32 and 36 to get 68.

$$\frac{68}{3^{2}}-\frac{8}{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{68}{9}-\frac{8}{3}$$

Subtract \frac{8}{3} from \frac{68}{9} to get \frac{44}{9}.

$$\frac{44}{9}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{3 ^ {2}} = 4\frac{8}{9} = 4.888888888888889$$