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

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

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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}.

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{3\sqrt{5}}{6}$$

Divide 3\sqrt{5} by 6 to get \frac{1}{2}\sqrt{5}.

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