Solve 8/3-sqrt{11}

$$\frac { 8 } { 3 - \sqrt { 11 } }$$

Evaluate

$$-4\sqrt{11}-12\approx -25.266499161$$

Solution Steps

Rationalize the denominator of \frac{8}{3-\sqrt{11}} by multiplying numerator and denominator by 3+\sqrt{11}.

$$\frac{8\left(3+\sqrt{11}\right)}{\left(3-\sqrt{11}\right)\left(3+\sqrt{11}\right)}$$

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}.

$$\frac{8\left(3+\sqrt{11}\right)}{3^{2}-\left(\sqrt{11}\right)^{2}}$$

Square 3. Square \sqrt{11}.

$$\frac{8\left(3+\sqrt{11}\right)}{9-11}$$

Subtract 11 from 9 to get -2.

$$\frac{8\left(3+\sqrt{11}\right)}{-2}$$

Divide 8\left(3+\sqrt{11}\right) by -2 to get -4\left(3+\sqrt{11}\right).

$$-4\left(3+\sqrt{11}\right)$$

Use the distributive property to multiply -4 by 3+\sqrt{11}.

$$-12-4\sqrt{11}$$