Solve 4*(2/3sqrt{21})^2+1

$$4 \times ( \frac { 2 } { 3 } \sqrt { 21 } ) ^ { 2 } + 1$$

Evaluate

$$\frac{115}{3}\approx 38.333333333$$

Solution Steps

Expand \left(\frac{2}{3}\sqrt{21}\right)^{2}.

$$4\times \left(\frac{2}{3}\right)^{2}\left(\sqrt{21}\right)^{2}+1$$

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

$$4\times \frac{4}{9}\left(\sqrt{21}\right)^{2}+1$$

The square of \sqrt{21} is 21.

$$4\times \frac{4}{9}\times 21+1$$

Multiply \frac{4}{9} and 21 to get \frac{28}{3}.

$$4\times \frac{28}{3}+1$$

Multiply 4 and \frac{28}{3} to get \frac{112}{3}.

$$\frac{112}{3}+1$$

Add \frac{112}{3} and 1 to get \frac{115}{3}.

$$\frac{115}{3}$$

Factor

$$\frac{5 \cdot 23}{3} = 38\frac{1}{3} = 38.333333333333336$$