Solve 10/sqrt{11-1}

$$\frac { 10 } { \sqrt { 11 } - 1 }$$

Evaluate

$$\sqrt{11}+1\approx 4.31662479$$

Solution Steps

Rationalize the denominator of \frac{10}{\sqrt{11}-1} by multiplying numerator and denominator by \sqrt{11}+1.

$$\frac{10\left(\sqrt{11}+1\right)}{\left(\sqrt{11}-1\right)\left(\sqrt{11}+1\right)}$$

Consider \left(\sqrt{11}-1\right)\left(\sqrt{11}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{10\left(\sqrt{11}+1\right)}{\left(\sqrt{11}\right)^{2}-1^{2}}$$

Square \sqrt{11}. Square 1.

$$\frac{10\left(\sqrt{11}+1\right)}{11-1}$$

Subtract 1 from 11 to get 10.

$$\frac{10\left(\sqrt{11}+1\right)}{10}$$

Cancel out 10 and 10.

$$\sqrt{11}+1$$