Solve frac{3sqrt{2}*2sqrt{5}}{9}-2sqrt{5}*1/3sqrt{8}

$$\frac { 3 \sqrt { 2 } \cdot 2 \sqrt { 5 } } { 9 } - 2 \sqrt { 5 } \cdot \frac { 1 } { 3 } \sqrt { 8 }$$

Evaluate

$$-\frac{2\sqrt{10}}{3}\approx -2.108185107$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}\sqrt{5}}{9}-2\sqrt{5}\times \frac{1}{3}\sqrt{8}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{6\sqrt{10}}{9}-2\sqrt{5}\times \frac{1}{3}\sqrt{8}$$

Divide 6\sqrt{10} by 9 to get \frac{2}{3}\sqrt{10}.

$$\frac{2}{3}\sqrt{10}-2\sqrt{5}\times \frac{1}{3}\sqrt{8}$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$\frac{2}{3}\sqrt{10}-\frac{2}{3}\sqrt{5}\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2}{3}\sqrt{10}-\frac{2}{3}\sqrt{5}\times 2\sqrt{2}$$

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

$$\frac{2}{3}\sqrt{10}-\frac{2\times 2}{3}\sqrt{5}\sqrt{2}$$

Multiply 2 and 2 to get 4.

$$\frac{2}{3}\sqrt{10}-\frac{4}{3}\sqrt{5}\sqrt{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{2}{3}\sqrt{10}-\frac{4}{3}\sqrt{10}$$

Combine \frac{2}{3}\sqrt{10} and -\frac{4}{3}\sqrt{10} to get -\frac{2}{3}\sqrt{10}.

$$-\frac{2}{3}\sqrt{10}$$