Chapter 10.3, Problem 3STP

For Exercises 1-6, choose the correct letter.

What is the simplified form of $4\sqrt{3}-\sqrt{27}$?

A $-5\sqrt{3}$

B. $-7\sqrt{3}$

C. $\sqrt{3}$

D $-\sqrt{9}$

To determine

To find: the difference of the expression.

Answer to Problem 3STP

The difference of the expression is $\sqrt{3}$ .

Explanation of Solution

Given information:

The expression is $4\sqrt{3}-\sqrt{27}$ .

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

  $\begin{array}{l}4\sqrt{3}-\sqrt{27}=4\sqrt{3}-3\sqrt{3}\text{ [simplify]}\\ 4\sqrt{3}-\sqrt{27}=\sqrt{3}\left(4-3\right)\text{ [take common ]}\\ 4\sqrt{3}-\sqrt{27}=\sqrt{3}\text{ [add]}\end{array}$

Thus, The sum of the expression is $\sqrt{3}$ .