Solve frac{2sqrt{16}}{3}-2sqrt{2}*frac{sqrt{3}}{3}-1

$$\frac { 2 \sqrt { 16 } } { 3 } - 2 \sqrt { 2 } \times \frac { \sqrt { 3 } } { 3 } - 1$$

Evaluate

$$\frac{5-2\sqrt{6}}{3}\approx 0.033673505$$

Short Solution Steps

Calculate the square root of 16 and get 4.

$$\frac{2\times 4}{3}-2\sqrt{2}\times \frac{\sqrt{3}}{3}-1$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}-2\sqrt{2}\times \frac{\sqrt{3}}{3}-1$$

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

$$\frac{8}{3}-\frac{2\sqrt{3}}{3}\sqrt{2}-1$$

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

$$\frac{8}{3}-\frac{2\sqrt{3}\sqrt{2}}{3}-1$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Since \frac{8}{3} and \frac{2\sqrt{6}}{3} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

Since \frac{8+2\sqrt{6}}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the calculations in 8+2\sqrt{6}-3.

$$\frac{5+2\sqrt{6}}{3}$$

Factor

$$\frac{5 - 2 \sqrt{6}}{3} = 0.03367350481121475$$