Chapter 10.3, Problem 20P

Simplify each quotient.

$\frac{8}{\sqrt{3}+1}$

To determine

To find: the quotient of the expression.

Answer to Problem 20P

The quotient of the expression is $4\left(\sqrt{3}-1\right)$ .

Explanation of Solution

Given information:

The expression is $\frac{8}{\sqrt{3}+1}$ .

Calculation: to find the quotient of the expression, first multiply the conjugate of denominator and then simplify,

  $\begin{array}{l}\frac{8}{\sqrt{3}+1}=\frac{8\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\text{ [multiply by conjugate of denominator]}\\ \frac{8}{\sqrt{3}+1}=\frac{8\left(\sqrt{3}-1\right)}{3-1}\text{ [multiply]}\\ \frac{8}{\sqrt{3}+1}=4\left(\sqrt{3}-1\right)\text{ [simplify]}\end{array}$

Thus, The quotient of the expression is $4\left(\sqrt{3}-1\right)$ .