Solve =(2/3+sqrt{11}+tansqrt{11}):2

$$= ( \frac { 2 } { 3 + \sqrt { 11 } } + \tan \sqrt { 11 } ) : 2$$

Evaluate

$$\frac{\sqrt{11}}{2}-1.4710246179565642265\approx 0.187287777$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{2}{3 + \sqrt{11}} + 0.057950764086871547)} / 2$$

Rationalize the denominator of \frac{2}{3+\sqrt{11}} by multiplying numerator and denominator by 3-\sqrt{11}.

$$\frac{\frac{2\left(3-\sqrt{11}\right)}{\left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right)}+0.057950764086871547}{2}$$

Consider \left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\frac{2\left(3-\sqrt{11}\right)}{3^{2}-\left(\sqrt{11}\right)^{2}}+0.057950764086871547}{2}$$

Square 3. Square \sqrt{11}.

$$\frac{\frac{2\left(3-\sqrt{11}\right)}{9-11}+0.057950764086871547}{2}$$

Subtract 11 from 9 to get -2.

$$\frac{\frac{2\left(3-\sqrt{11}\right)}{-2}+0.057950764086871547}{2}$$

Cancel out -2 and -2.

$$\frac{-\left(3-\sqrt{11}\right)+0.057950764086871547}{2}$$

To find the opposite of 3-\sqrt{11}, find the opposite of each term.

$$\frac{-3-\left(-\sqrt{11}\right)+0.057950764086871547}{2}$$

The opposite of -\sqrt{11} is \sqrt{11}.

$$\frac{-3+\sqrt{11}+0.057950764086871547}{2}$$

Add -3 and 0.057950764086871547 to get -2.942049235913128453.

$$\frac{-2.942049235913128453+\sqrt{11}}{2}$$