Solve frac{sqrt{50}}{3sqrt{8}}

$$\frac { \sqrt { 50 } } { 3 \sqrt { 8 } }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

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}.

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

Multiply 3 and 2 to get 6.

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

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$