To simplify the expression \( 4\sqrt{8} - \sqrt{32} \), we first need to simplify the square roots.

### Step 1: Simplify each square root
- \( \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \)
- \( \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \)

### Step 2: Substitute back into the original expression
\[
4\sqrt{8} - \sqrt{32} = 4(2\sqrt{2}) - 4\sqrt{2}
\]
\[
= 8\sqrt{2} - 4\sqrt{2}
\]

### Step 3: Combine like terms
\[
8\sqrt{2} - 4\sqrt{2} = (8 - 4)\sqrt{2} = 4\sqrt{2}
\]

Thus, the simplified expression is \( 4\sqrt{2} \).

Would you like more details on any of the steps, or do you have any other questions?

---

Here are 5 related questions:
1. How would you simplify \( \sqrt{50} + \sqrt{18} \)?
2. What is \( 5\sqrt{12} - 3\sqrt{27} \)?
3. Can you simplify \( 6\sqrt{2} + 3\sqrt{8} \)?
4. What happens if you have \( 7\sqrt{20} - 2\sqrt{5} \)?
5. How would you add \( 9\sqrt{45} + \sqrt{5} \)?

**Tip**: Always try to express square roots in terms of their simplest form by factoring out perfect squares.

Learn how to simplify the expression 4√8 - √32 by breaking down the radicals and combining like terms. This step-by-step solution covers fundamental algebraic concepts such as the properties of square roots and arithmetic operations with radicals, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation