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Chapter 5: Problem 45

Perform the indicated operation. Simplify the answer when possible. \(4 \sqrt{2}-5 \sqrt{2}+8 \sqrt{2}\)

Short Answer

Expert verified
\The simplified form of \(4 \sqrt{2}-5 \sqrt{2}+8 \sqrt{2}\) is \(7 \sqrt{2}\)

Step by step solution

01

Identify Like Terms

The expression given is \(4 \sqrt{2}-5 \sqrt{2}+8 \sqrt{2}\). Notice that \(\sqrt{2}\) can be seen as a common 'term' in all three parts of the expression. Therefore, \(4 \sqrt{2}\), -\(5 \sqrt{2}\), \(8 \sqrt{2}\) are like terms because they all contain the \(\sqrt{2}\) factor.
02

Combine Like Terms

We can combine these like terms by adding or subtracting their coefficients (the numbers in front of the \(\sqrt{2}\) ). That is, 4 (from \(4 \sqrt{2}\) ) minus 5 (from -\(5 \sqrt{2}\) ) plus 8 (from \(8 \sqrt{2}\) ) equals 7.
03

Write the Final Answer

The final answer is thus \(7 \sqrt{2}\), achieved by combining the coefficients of the like terms and then putting it with the common term \(\sqrt{2}\).

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