Solve 2*2frac{sqrt{5}}{2sqrt{3}}=

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

Evaluate

$$\frac{2\sqrt{15}}{3}\approx 2.581988897$$

Solution Steps

Multiply 2 and 2 to get 4.

$$4\times \frac{\sqrt{5}}{2\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4\times \frac{\sqrt{5}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\times \frac{\sqrt{5}\sqrt{3}}{2\times 3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{15}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$4\times \frac{\sqrt{15}}{6}$$

Express 4\times \frac{\sqrt{15}}{6} as a single fraction.

$$\frac{4\sqrt{15}}{6}$$

Divide 4\sqrt{15} by 6 to get \frac{2}{3}\sqrt{15}.

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