Solve 8/sqrt{13-3}

$$\frac { 8 } { \sqrt { 13 } - 3 }$$

Evaluate

$$2\left(\sqrt{13}+3\right)\approx 13.211102551$$

Solution Steps

Rationalize the denominator of \frac{8}{\sqrt{13}-3} by multiplying numerator and denominator by \sqrt{13}+3.

$$\frac{8\left(\sqrt{13}+3\right)}{\left(\sqrt{13}-3\right)\left(\sqrt{13}+3\right)}$$

Consider \left(\sqrt{13}-3\right)\left(\sqrt{13}+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}.

$$\frac{8\left(\sqrt{13}+3\right)}{\left(\sqrt{13}\right)^{2}-3^{2}}$$

Square \sqrt{13}. Square 3.

$$\frac{8\left(\sqrt{13}+3\right)}{13-9}$$

Subtract 9 from 13 to get 4.

$$\frac{8\left(\sqrt{13}+3\right)}{4}$$

Divide 8\left(\sqrt{13}+3\right) by 4 to get 2\left(\sqrt{13}+3\right).

$$2\left(\sqrt{13}+3\right)$$

Use the distributive property to multiply 2 by \sqrt{13}+3.

$$2\sqrt{13}+6$$