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

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

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

Solution Steps

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

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

The square of \sqrt{15} is 15.

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

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}.

$$\frac{2\sqrt{5}\sqrt{5}\sqrt{3}}{15}$$

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

$$\frac{2\times 5\sqrt{3}}{15}$$

Multiply 2 and 5 to get 10.

$$\frac{10\sqrt{3}}{15}$$

Divide 10\sqrt{3} by 15 to get \frac{2}{3}\sqrt{3}.

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