Let's break down the expression step by step:

The given expression is:

\[
4\sqrt{18} \times 5\sqrt{50} \div 2\sqrt{8}
\]

### Step 1: Simplify each square root term

- \(\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}\)
- \(\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}\)
- \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\)

Now, substitute these simplified terms back into the expression:

\[
4(3\sqrt{2}) \times 5(5\sqrt{2}) \div 2(2\sqrt{2})
\]

### Step 2: Simplify the coefficients

The expression becomes:

\[
(12\sqrt{2}) \times (25\sqrt{2}) \div (4\sqrt{2})
\]

### Step 3: Multiply and divide

Now, multiply \(12\sqrt{2}\) by \(25\sqrt{2}\):

\[
12 \times 25 = 300 \quad \text{and} \quad \sqrt{2} \times \sqrt{2} = 2
\]

So, the result of the multiplication is:

\[
300 \times 2 = 600
\]

Next, divide this by \(4\sqrt{2}\):

\[
\frac{600}{4\sqrt{2}} = \frac{600}{4} \times \frac{1}{\sqrt{2}} = 150 \times \frac{1}{\sqrt{2}}
\]

To rationalize the denominator:

\[
150 \times \frac{1}{\sqrt{2}} = 150 \times \frac{\sqrt{2}}{2} = \frac{150\sqrt{2}}{2} = 75\sqrt{2}
\]

### Final Answer:

The simplified result is:

\[
75\sqrt{2}
\]

Would you like further details or have any questions?

Here are 5 questions to consider based on this explanation:
1. What steps would you take to simplify larger square roots?
2. How do you rationalize denominators involving square roots?
3. What are some common mistakes to avoid when simplifying radical expressions?
4. Can you apply these steps to an expression like \(3\sqrt{12} \times 4\sqrt{27} \div 2\sqrt{3}\)?
5. How does multiplying radicals compare with adding or subtracting them?

**Tip:** Always look for perfect square factors when simplifying square roots, as this can make the calculations much easier.

Learn how to simplify the radical expression 4√18 * 5√50 : 2√8 with a step-by-step solution. This problem covers algebraic concepts like simplifying radicals, multiplying and dividing radicals, and rationalizing denominators. Suitable for Grades 8-10 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