Solve 28/sqrt{11+2}

$$\frac { 28 } { \sqrt { 11 } + 2 }$$

Evaluate

$$4\left(\sqrt{11}-2\right)\approx 5.266499161$$

Solution Steps

Rationalize the denominator of \frac{28}{\sqrt{11}+2} by multiplying numerator and denominator by \sqrt{11}-2.

$$\frac{28\left(\sqrt{11}-2\right)}{\left(\sqrt{11}+2\right)\left(\sqrt{11}-2\right)}$$

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

$$\frac{28\left(\sqrt{11}-2\right)}{\left(\sqrt{11}\right)^{2}-2^{2}}$$

Square \sqrt{11}. Square 2.

$$\frac{28\left(\sqrt{11}-2\right)}{11-4}$$

Subtract 4 from 11 to get 7.

$$\frac{28\left(\sqrt{11}-2\right)}{7}$$

Divide 28\left(\sqrt{11}-2\right) by 7 to get 4\left(\sqrt{11}-2\right).

$$4\left(\sqrt{11}-2\right)$$

Use the distributive property to multiply 4 by \sqrt{11}-2.

$$4\sqrt{11}-8$$