Solve 4/sqrt{13-3}

$$\frac{ 4 }{ \sqrt{ 13 } -3 }$$

Evaluate

$$\sqrt{13}+3\approx 6.605551275$$

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{13}-3} by multiplying numerator and denominator by \sqrt{13}+3.

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

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}.

$$\frac{4\left(\sqrt{13}+3\right)}{\left(\sqrt{13}\right)^{2}-3^{2}}$$

Square \sqrt{13}. Square 3.

$$\frac{4\left(\sqrt{13}+3\right)}{13-9}$$

Subtract 9 from 13 to get 4.

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

Cancel out 4 and 4.

$$\sqrt{13}+3$$