Solve frac{1sqrt{15}}{2sqrt{5}}

$$\frac { 1 \sqrt { 15 } } { 2 \sqrt { 5 } }$$

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Cancel out 1 in both numerator and denominator.

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

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

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

The square of \sqrt{5} is 5.

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

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}.

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

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

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

Multiply 2 and 5 to get 10.

$$\frac{5\sqrt{3}}{10}$$

Divide 5\sqrt{3} by 10 to get \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\sqrt{3}$$