Chapter 10.3, Problem 28P

Error Analysis A student multiplied the radical expressions shown at the right. What mistake did the student make? What is the simplified form of the radical? $\begin{array}{l}\sqrt{3}\left(\sqrt{3}+\sqrt{6}\right)\\ =\sqrt{9}+\sqrt{18}\\ =6\sqrt{2}\end{array}$

To determine

To find: the simplest form of the radical expression.

Answer to Problem 28P

The simplest form of the radical expression is $3+3\sqrt{2}$ .

Explanation of Solution

Given information:

The radical expression is $\sqrt{3}\left(\sqrt{3}+\sqrt{6}\right)$ .

Calculation: to find the simplest form of the radical expression, first multiply and then simplify,

  $\begin{array}{l}\sqrt{3}\left(\sqrt{3}+\sqrt{6}\right)=\sqrt{9}+\sqrt{18}\text{ [multiply]}\\ \sqrt{3}\left(\sqrt{3}+\sqrt{6}\right)=3+3\sqrt{2}\text{ [simplify]}\end{array}$

Thus, The simplest form of the radical expression is $3+3\sqrt{2}$ .