Express in simplest radical form.

minus, square root of, 2, end square root, minus, 8, square root of, 2, end square root


The expression given is:

\[
-\sqrt{2} - 8\sqrt{2}
\]

### Step 1: Identify like terms
Both terms involve the square root of 2 (\(\sqrt{2}\)). Since they are like terms, we can combine them.

### Step 2: Combine the like terms
When combining, factor out the common \(\sqrt{2}\):

\[
-\sqrt{2} - 8\sqrt{2} = (-1 - 8)\sqrt{2}
\]

### Step 3: Simplify the expression
Add the coefficients:

\[
(-1 - 8)\sqrt{2} = -9\sqrt{2}
\]

So, the expression in its simplest radical form is:

\[
\boxed{-9\sqrt{2}}
\]

Would you like any further clarification or have other questions?

Here are some related questions:
1. How do you combine like radical terms?
2. What happens if the radicals are different?
3. How do you simplify an expression with multiple different radicals?
4. Can you add or subtract radicals with different coefficients?
5. How do you handle negative signs when simplifying radicals?

**Tip:** Always factor out the common radical when combining like terms to simplify the expression efficiently!

Learn how to simplify the expression -√2 - 8√2 to its simplest radical form with step-by-step instructions. Understand how to combine like terms involving radicals efficiently. Suitable for high school students studying simplification of radicals and algebraic expressions.

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