Solve 4^2+{left(4/3sqrt{3}right)}^2

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

Evaluate

$$\frac{64}{3}\approx 21.333333333$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16+\left(\frac{4}{3}\sqrt{3}\right)^{2}$$

Expand \left(\frac{4}{3}\sqrt{3}\right)^{2}.

$$16+\left(\frac{4}{3}\right)^{2}\left(\sqrt{3}\right)^{2}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$16+\frac{16}{9}\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16+\frac{16}{9}\times 3$$

Multiply \frac{16}{9} and 3 to get \frac{16}{3}.

$$16+\frac{16}{3}$$

Add 16 and \frac{16}{3} to get \frac{64}{3}.

$$\frac{64}{3}$$

Factor

$$\frac{2 ^ {6}}{3} = 21\frac{1}{3} = 21.333333333333332$$