Solve 4^2/3^2*2sqrt{5}*6=

$$\frac{ { 4 }^{ 2 } }{ { 3 }^{ 2 } \times 2 \sqrt{ 5 } } \times 6=$$

Evaluate

$$\frac{16\sqrt{5}}{15}\approx 2.385139176$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$6\times \frac{16}{2\times 3^{2}\sqrt{5}}$$

Calculate 3 to the power of 2 and get 9.

$$6\times \frac{16}{2\times 9\sqrt{5}}$$

Multiply 2 and 9 to get 18.

$$6\times \frac{16}{18\sqrt{5}}$$

Rationalize the denominator of \frac{16}{18\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$6\times \frac{16\sqrt{5}}{18\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$6\times \frac{16\sqrt{5}}{18\times 5}$$

Cancel out 2 in both numerator and denominator.

$$6\times \frac{8\sqrt{5}}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$6\times \frac{8\sqrt{5}}{45}$$

Express 6\times \frac{8\sqrt{5}}{45} as a single fraction.

$$\frac{6\times 8\sqrt{5}}{45}$$

Multiply 6 and 8 to get 48.

$$\frac{48\sqrt{5}}{45}$$

Divide 48\sqrt{5} by 45 to get \frac{16}{15}\sqrt{5}.

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