Question

Simplify the expression. $$3 \sqrt{7}-2 \sqrt{7}$$

Short answer

\[3 \sqrt{7}-2 \sqrt{7} = \sqrt{7}\].

Step-by-step solution

Identify like terms

In the given expression, \[3 \sqrt{7}\] and \[-2 \sqrt{7}\] are like terms because they both contain the square root of 7.

Combine like terms

Like terms can be combined by adding or subtracting the numbers in front of the like terms. In other words, you add or subtract the coefficients. Here, subtract 2 from 3: \(3-2=1\), Therefore, \[3 \sqrt{7} - 2 \sqrt{7} = \sqrt{7}\].

Write the final expression

The simplified expression is \[1 \sqrt{7}\], but typically we write this simply as \[\sqrt{7}\]. Thus, \[3 \sqrt{7}-2 \sqrt{7} = \sqrt{7}\].