Solve (2^2/sqrt{3}*4/sqrt{5})

$$( \frac { 2 ^ { 2 } } { \sqrt { 3 } } \cdot \frac { 4 } { \sqrt { 5 } } )$$

Evaluate

$$\frac{16\sqrt{15}}{15}\approx 4.131182236$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Rationalize the denominator of \frac{4}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

Multiply \frac{4\sqrt{3}}{3} times \frac{4\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 4 and 4 to get 16.

$$\frac{16\sqrt{3}\sqrt{5}}{3\times 5}$$

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

$$\frac{16\sqrt{15}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{16\sqrt{15}}{15}$$