Solve 60/sqrt{3+1}

$$\frac { 60 } { \sqrt { 3 } + 1 }$$

Evaluate

$$30\left(\sqrt{3}-1\right)\approx 21.961524227$$

Solution Steps

Rationalize the denominator of \frac{60}{\sqrt{3}+1} by multiplying numerator and denominator by \sqrt{3}-1.

$$\frac{60\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}$$

Consider \left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{60\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}$$

Square \sqrt{3}. Square 1.

$$\frac{60\left(\sqrt{3}-1\right)}{3-1}$$

Subtract 1 from 3 to get 2.

$$\frac{60\left(\sqrt{3}-1\right)}{2}$$

Divide 60\left(\sqrt{3}-1\right) by 2 to get 30\left(\sqrt{3}-1\right).

$$30\left(\sqrt{3}-1\right)$$

Use the distributive property to multiply 30 by \sqrt{3}-1.

$$30\sqrt{3}-30$$