Chapter 10.3, Problem 7P

Simplify each sum or difference.

$4\sqrt{7}-\sqrt{63}$

To determine

To find: the difference of the expression.

Answer to Problem 7P

The difference of the expression is $\sqrt{7}$ .

Explanation of Solution

Given information:

The expression is $4\sqrt{7}-\sqrt{63}$ .

Calculation: to find the difference of the expression, first simplify and then take the common and then subtract and simplify,

  $\begin{array}{l}4\sqrt{7}-\sqrt{63}=4\sqrt{7}-3\sqrt{7}\text{ [simplify]}\\ 4\sqrt{7}-\sqrt{63}=\sqrt{7}\left(4-3\right)\text{ [take common ]}\\ 4\sqrt{7}-\sqrt{63}=\sqrt{7}\text{ [subtract]}\end{array}$

Thus, The difference of the expression is $\sqrt{7}$ .