Solve sqrt{5}frac{sqrt{2}}{15sqrt{5}}

$$\sqrt{ 5 } \frac { \sqrt{ 2 } } { 15 \sqrt{ 5 } }$$

Evaluate

$$\frac{\sqrt{2}}{15}\approx 0.094280904$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}}{15\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\sqrt{5}\times \frac{\sqrt{2}\sqrt{5}}{15\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

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

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

$$\sqrt{5}\times \frac{\sqrt{10}}{15\times 5}$$

Multiply 15 and 5 to get 75.

$$\sqrt{5}\times \frac{\sqrt{10}}{75}$$

Express \sqrt{5}\times \frac{\sqrt{10}}{75} as a single fraction.

$$\frac{\sqrt{5}\sqrt{10}}{75}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{\sqrt{5}\sqrt{5}\sqrt{2}}{75}$$

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

$$\frac{5\sqrt{2}}{75}$$

Divide 5\sqrt{2} by 75 to get \frac{1}{15}\sqrt{2}.

$$\frac{1}{15}\sqrt{2}$$