Solve 2/sqrt{11+3}

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

Evaluate

$$\sqrt{11}-3\approx 0.31662479$$

Solution Steps

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

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

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

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

Square \sqrt{11}. Square 3.

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

Subtract 9 from 11 to get 2.

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

Cancel out 2 and 2.

$$\sqrt{11}-3$$