Solve 9/2-sqrt{3}

$$\frac{ 9 }{ 2- \sqrt{ 3 } }$$

Evaluate

$$9\left(\sqrt{3}+2\right)\approx 33.588457268$$

Solution Steps

Rationalize the denominator of \frac{9}{2-\sqrt{3}} by multiplying numerator and denominator by 2+\sqrt{3}.

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

Consider \left(2-\sqrt{3}\right)\left(2+\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}.

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

Square 2. Square \sqrt{3}.

$$\frac{9\left(2+\sqrt{3}\right)}{4-3}$$

Subtract 3 from 4 to get 1.

$$\frac{9\left(2+\sqrt{3}\right)}{1}$$

Anything divided by one gives itself.

$$9\left(2+\sqrt{3}\right)$$

Use the distributive property to multiply 9 by 2+\sqrt{3}.

$$18+9\sqrt{3}$$