Let's simplify the expression step by step:

### Given:
\[
4\sqrt{32} \cdot \sqrt{4}
\]

### Step 1: Simplify \(\sqrt{32}\)
We can simplify \(\sqrt{32}\) as follows:
\[
\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]

### Step 2: Simplify \(\sqrt{4}\)
\(\sqrt{4} = 2\)

### Step 3: Substitute the simplified expressions back into the equation
\[
4\sqrt{32} \cdot \sqrt{4} = 4(4\sqrt{2}) \cdot 2 = 16\sqrt{2} \cdot 2 = 32\sqrt{2}
\]

Thus, the simplified expression is:
\[
32\sqrt{2}
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:
1. Simplify \(3\sqrt{18} \cdot \sqrt{9}\)
2. Solve \(5\sqrt{50} \cdot \sqrt{2}\)
3. Simplify \(\sqrt{72} \cdot \sqrt{8}\)
4. What is the value of \(6\sqrt{27} \cdot \sqrt{3}\)?
5. Simplify \(\sqrt{12} \cdot 2\sqrt{3}\)

**Tip:** When simplifying square roots, try to factor out perfect squares to make the expression easier to handle.

Learn how to simplify the expression 4√32 ⋅ √4 using properties of square roots. This step-by-step solution explains simplifying radicals and multiplication of square roots, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation