Solve 3-frac{2sqrt{2}}{3}-9*-1/3+4*2sqrt{2}

$$3 - \frac { 2 \sqrt { 2 } } { 3 } - 9 \cdot - \frac { 1 } { 3 } + 4 \cdot 2 \sqrt { 2 }$$

Evaluate

$$\frac{22\sqrt{2}}{3}+6\approx 16.370899457$$

Short Solution Steps

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

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

Since \frac{3\times 3}{3} and \frac{2\sqrt{2}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 3-2\sqrt{2}.

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

Express 9\left(-\frac{1}{3}\right) as a single fraction.

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

Multiply 9 and -1 to get -9.

$$\frac{9-2\sqrt{2}}{3}-\frac{-9}{3}+2\times 4\sqrt{2}$$

Divide -9 by 3 to get -3.

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

The opposite of -3 is 3.

$$\frac{9-2\sqrt{2}}{3}+3+2\times 4\sqrt{2}$$

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

$$\frac{9-2\sqrt{2}}{3}+\frac{3\times 3}{3}+2\times 4\sqrt{2}$$

Since \frac{9-2\sqrt{2}}{3} and \frac{3\times 3}{3} have the same denominator, add them by adding their numerators.

$$\frac{9-2\sqrt{2}+3\times 3}{3}+2\times 4\sqrt{2}$$

Do the multiplications in 9-2\sqrt{2}+3\times 3.

$$\frac{9-2\sqrt{2}+9}{3}+2\times 4\sqrt{2}$$

Do the calculations in 9-2\sqrt{2}+9.

$$\frac{18-2\sqrt{2}}{3}+2\times 4\sqrt{2}$$

Multiply 2 and 4 to get 8.

$$\frac{18-2\sqrt{2}}{3}+8\sqrt{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8\sqrt{2} times \frac{3}{3}.

$$\frac{18-2\sqrt{2}}{3}+\frac{3\times 8\sqrt{2}}{3}$$

Since \frac{18-2\sqrt{2}}{3} and \frac{3\times 8\sqrt{2}}{3} have the same denominator, add them by adding their numerators.

$$\frac{18-2\sqrt{2}+3\times 8\sqrt{2}}{3}$$

Do the multiplications in 18-2\sqrt{2}+3\times 8\sqrt{2}.

$$\frac{18-2\sqrt{2}+24\sqrt{2}}{3}$$

Do the calculations in 18-2\sqrt{2}+24\sqrt{2}.

$$\frac{18+22\sqrt{2}}{3}$$

Factor

$$\frac{2 {(11 \sqrt{2} + 9)}}{3} = 16.370899457402697$$