Solve 13/3+sqrt{11}

$$\frac { 13 } { 3 + \sqrt { 11 } }$$

Evaluate

$$\frac{13\left(\sqrt{11}-3\right)}{2}\approx 2.058061137$$

Solution Steps

Rationalize the denominator of \frac{13}{3+\sqrt{11}} by multiplying numerator and denominator by 3-\sqrt{11}.

$$\frac{13\left(3-\sqrt{11}\right)}{\left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right)}$$

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}.

$$\frac{13\left(3-\sqrt{11}\right)}{3^{2}-\left(\sqrt{11}\right)^{2}}$$

Square 3. Square \sqrt{11}.

$$\frac{13\left(3-\sqrt{11}\right)}{9-11}$$

Subtract 11 from 9 to get -2.

$$\frac{13\left(3-\sqrt{11}\right)}{-2}$$

Use the distributive property to multiply 13 by 3-\sqrt{11}.

$$\frac{39-13\sqrt{11}}{-2}$$