Solve sqrt{4^2-(2/3sqrt{11})^2}

$$\sqrt { 4 ^ { 2 } - ( \frac { 2 } { 3 } \sqrt { 11 } ) ^ { 2 } }$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16-\left(\frac{2}{3}\sqrt{11}\right)^{2}}$$

Expand \left(\frac{2}{3}\sqrt{11}\right)^{2}.

$$\sqrt{16-\left(\frac{2}{3}\right)^{2}\left(\sqrt{11}\right)^{2}}$$

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

$$\sqrt{16-\frac{4}{9}\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\sqrt{16-\frac{4}{9}\times 11}$$

Multiply \frac{4}{9} and 11 to get \frac{44}{9}.

$$\sqrt{16-\frac{44}{9}}$$

Subtract \frac{44}{9} from 16 to get \frac{100}{9}.

$$\sqrt{\frac{100}{9}}$$

Rewrite the square root of the division \frac{100}{9} as the division of square roots \frac{\sqrt{100}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$