Solve frac{2sqrt{3}}{sqrt{15}}

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

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{2\sqrt{3}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{5}}{15}$$

Divide 6\sqrt{5} by 15 to get \frac{2}{5}\sqrt{5}.

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