Solve frac{sqrt{8}}{3sqrt{40}}divsqrt{5}

$$\frac { \sqrt { 8 } } { 3 \sqrt { 40 } } \div \sqrt { 5 }$$

Evaluate

$$\frac{1}{15}\approx 0.066666667$$

Solution Steps

Express \frac{\frac{\sqrt{8}}{3\sqrt{40}}}{\sqrt{5}} as a single fraction.

$$\frac{\sqrt{8}}{3\sqrt{40}\sqrt{5}}$$

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}.

$$\frac{2\sqrt{2}}{3\sqrt{40}\sqrt{5}}$$

Factor 40=5\times 8. Rewrite the square root of the product \sqrt{5\times 8} as the product of square roots \sqrt{5}\sqrt{8}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Multiply 3 and 5 to get 15.

$$\frac{2\sqrt{2}}{15\sqrt{8}}$$

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}.

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

Multiply 15 and 2 to get 30.

$$\frac{2\sqrt{2}}{30\sqrt{2}}$$

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

$$\frac{1}{15}$$

Factor

$$\frac{1}{3 \cdot 5} = 0.06666666666666667$$