Solve frac{sqrt{8}}{3sqrt{4}}*sqrt{5}

$$\frac { \sqrt { 8 } } { 3 \sqrt { 4 } } \times \sqrt { 5 }$$

Evaluate

$$\frac{\sqrt{10}}{3}\approx 1.054092553$$

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}.

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

Calculate the square root of 4 and get 2.

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

Multiply 3 and 2 to get 6.

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

Divide 2\sqrt{2} by 6 to get \frac{1}{3}\sqrt{2}.

$$\frac{1}{3}\sqrt{2}\sqrt{5}$$

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

$$\frac{1}{3}\sqrt{10}$$