Solve 13/4+sqrt{3}

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

Evaluate

$$4-\sqrt{3}\approx 2.267949192$$

Solution Steps

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

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

Consider \left(4+\sqrt{3}\right)\left(4-\sqrt{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}.

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

Square 4. Square \sqrt{3}.

$$\frac{13\left(4-\sqrt{3}\right)}{16-3}$$

Subtract 3 from 16 to get 13.

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

Cancel out 13 and 13.

$$4-\sqrt{3}$$