Solve frac{sqrt{5}}{sqrt{15}*5}=

$$\frac { \sqrt { 5 } } { \sqrt { 15 } \cdot 5 } =$$

Evaluate

$$\frac{\sqrt{3}}{15}\approx 0.115470054$$

Solution Steps

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

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

The square of \sqrt{15} is 15.

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

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{\sqrt{5}\sqrt{5}\sqrt{3}}{5\times 15}$$

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

$$\frac{5\sqrt{3}}{5\times 15}$$

Multiply 5 and 15 to get 75.

$$\frac{5\sqrt{3}}{75}$$

Divide 5\sqrt{3} by 75 to get \frac{1}{15}\sqrt{3}.

$$\frac{1}{15}\sqrt{3}$$