Let's simplify the expression:

\[
\sqrt{18a} - \sqrt{\frac{1}{2}a}
\]

### Step 1: Simplify \(\sqrt{18a}\)

We can break down \(\sqrt{18a}\) as:

\[
\sqrt{18a} = \sqrt{9 \cdot 2 \cdot a} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{a} = 3\sqrt{2a}
\]

### Step 2: Simplify \(\sqrt{\frac{1}{2}a}\)

Now simplify \(\sqrt{\frac{1}{2}a}\):

\[
\sqrt{\frac{1}{2}a} = \sqrt{\frac{a}{2}} = \frac{\sqrt{a}}{\sqrt{2}} = \frac{\sqrt{a}}{\sqrt{2}} = \frac{\sqrt{2a}}{2}
\]

### Step 3: Combine the results

Now, the expression becomes:

\[
3\sqrt{2a} - \frac{\sqrt{2a}}{2}
\]

We can factor out \(\sqrt{2a}\):

\[
\sqrt{2a} \left( 3 - \frac{1}{2} \right) = \sqrt{2a} \cdot \frac{5}{2}
\]

So, the simplified expression is:

\[
\frac{5}{2} \sqrt{2a}
\]

### Final Answer:

\[
\boxed{\frac{5}{2} \sqrt{2a}}
\]

Let me know if you need further clarification or have any other questions!

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Here are some related questions you might find interesting:

1. How do you simplify expressions involving square roots of variables?
2. What are some tricks for simplifying square roots with fractions?
3. How do you combine like terms under square roots?
4. How do you rationalize the denominator when simplifying square roots?
5. Can you simplify an expression like \(\sqrt{a} - \sqrt{b}\) if \(a \neq b\)?

**Tip**: Always look for perfect squares within a square root and factor them out to simplify!

Learn how to simplify the expression √18a - √(1/2 a) with detailed, step-by-step instructions. This solution covers simplifying square roots, factoring, and combining like terms, suitable for high school students (Grades 9-11).

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