Solve frac{sqrt{32}}{3}-frac{sqrt{8}}{5}

$$\frac { \sqrt { 32 } } { 3 } - \frac { \sqrt { 8 } } { 5 }$$

Evaluate

$$\frac{14\sqrt{2}}{15}\approx 1.319932658$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{4\sqrt{2}}{3}-\frac{\sqrt{8}}{5}$$

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}.

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

Combine \frac{4\sqrt{2}}{3} and -\frac{2\sqrt{2}}{5} to get \frac{14}{15}\sqrt{2}.

$$\frac{14}{15}\sqrt{2}$$