Solve 4/sqrt{3+2}

$$\frac { 4 } { \sqrt { 3 } + 2 }$$

Evaluate

$$8-4\sqrt{3}\approx 1.07179677$$

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{3}+2} by multiplying numerator and denominator by \sqrt{3}-2.

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

Consider \left(\sqrt{3}+2\right)\left(\sqrt{3}-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Square \sqrt{3}. Square 2.

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

Subtract 4 from 3 to get -1.

$$\frac{4\left(\sqrt{3}-2\right)}{-1}$$

Anything divided by -1 gives its opposite.

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

Use the distributive property to multiply -4 by \sqrt{3}-2.

$$-4\sqrt{3}+8$$