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Chapter 10: Problem 8

Perform the operation and simplify. Assume all variables represent non negative real numbers. $$10 \sqrt[3]{5}-2 \sqrt[3]{5}$$

Short Answer

Expert verified
The simplified expression is: \(8 \sqrt[3]{5}\).

Step by step solution

01

Identify Like Terms

In the given expression, we have two terms: \(10 \sqrt[3]{5}\) and \(-2 \sqrt[3]{5}\). Notice that both terms share the common factor of \(\sqrt[3]{5}\), which makes them like terms.
02

Combine Like Terms

To combine these like terms, we can add or subtract their coefficients. In this case, the coefficients are \(10\) and \(-2\). So, we have: \[10 \sqrt[3]{5} - 2 \sqrt[3]{5} = (10 - 2) \sqrt[3]{5}\]
03

Simplify the Expression

Now, simplify the expression by performing the subtraction: \[(10 - 2) \sqrt[3]{5} = 8 \sqrt[3]{5}\] The simplified expression is: \(8 \sqrt[3]{5}\).

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