Solve frac{sqrt{3}2}{3}-frac{sqrt{8}}{5}

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

Evaluate

$$\frac{2\sqrt{3}}{3}-\frac{2\sqrt{2}}{5}\approx 0.589015113$$

Short Solution Steps

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}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{2\sqrt{3}}{3} times \frac{5}{5}. Multiply \frac{2\sqrt{2}}{5} times \frac{3}{3}.

$$\frac{5\times 2\sqrt{3}}{15}-\frac{3\times 2\sqrt{2}}{15}$$

Since \frac{5\times 2\sqrt{3}}{15} and \frac{3\times 2\sqrt{2}}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 2\sqrt{3}-3\times 2\sqrt{2}}{15}$$

Do the multiplications in 5\times 2\sqrt{3}-3\times 2\sqrt{2}.

$$\frac{10\sqrt{3}-6\sqrt{2}}{15}$$

Factor

$$\frac{2 {(5 \sqrt{3} - 3 \sqrt{2})}}{15} = 0.5890151134300133$$