https://r2.erweima.ai/mathbot/image/1723305074810cu83jbik.jpg

Multiply. Write your answer in simplest form.

The expression you need to multiply is:

\[
-3\sqrt{2} \times (-4 - \sqrt{14})
\]

Let's distribute \(-3\sqrt{2}\) to each term inside the parentheses:

1. **Multiply \(-3\sqrt{2}\) by \(-4\):**

\[
-3\sqrt{2} \times -4 = 12\sqrt{2}
\]

2. **Multiply \(-3\sqrt{2}\) by \(-\sqrt{14}\):**

\[
-3\sqrt{2} \times -\sqrt{14} = 3\sqrt{28}
\]

Note that \(\sqrt{28}\) can be simplified:

\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]

So the second term becomes:

\[
3\sqrt{28} = 3 \times 2\sqrt{7} = 6\sqrt{7}
\]

Now, combine both terms:

\[
12\sqrt{2} + 6\sqrt{7}
\]

Thus, the final simplified answer is:

\[
\boxed{12\sqrt{2} + 6\sqrt{7}}
\]

Would you like more details or have any other questions?

Here are some related questions you might be interested in:

1. How do you multiply expressions involving square roots?
2. What are some common simplifications for square roots?
3. How do you distribute a term across a binomial?
4. Can square roots of different numbers be combined?
5. How do you handle negative signs in expressions involving square roots?
6. What is the difference between simplifying and expanding an expression?
7. How do you simplify a radical expression?
8. What is the significance of the order of operations in such expressions?

**Tip:** When multiplying expressions with square roots, always look for opportunities to simplify square roots before combining them.

Learn how to multiply and simplify the expression -3√2 * (-4 - √14) step-by-step with detailed explanations. This problem involves multiplication of expressions with square roots, including distributing terms across a binomial. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation