Simplify

square root 20w^2 x square root 5wx^2

Assume that all variables represent positive real numbers

To simplify the expression \(\sqrt{20w^2} \times \sqrt{5wx^2}\), let's break it down step by step:

### Step 1: Express the product of square roots as a single square root
By using the property of square roots, \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\), we can rewrite the expression:
\[
\sqrt{20w^2} \times \sqrt{5wx^2} = \sqrt{(20w^2) \times (5wx^2)}
\]

### Step 2: Multiply the terms under the square root
Now, multiply the terms inside the square root:
\[
(20w^2) \times (5wx^2) = 20 \times 5 \times w^2 \times w \times x^2 = 100w^3x^2
\]

So, we have:
\[
\sqrt{100w^3x^2}
\]

### Step 3: Simplify the square root
Now, simplify the square root by breaking it into factors that can be simplified:
\[
\sqrt{100w^3x^2} = \sqrt{100} \times \sqrt{w^3} \times \sqrt{x^2}
\]
We know that:
\[
\sqrt{100} = 10, \quad \sqrt{w^3} = w\sqrt{w}, \quad \text{and} \quad \sqrt{x^2} = x
\]

### Step 4: Combine the simplified parts
Now, put everything together:
\[
10 \times w\sqrt{w} \times x = 10wx\sqrt{w}
\]

### Final Simplified Expression:
The simplified form of \(\sqrt{20w^2} \times \sqrt{5wx^2}\) is:
\[
10wx\sqrt{w}
\]

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Would you like further clarification or more details?

Here are 5 related questions to consider:
1. How do you simplify more complex square root expressions?
2. How do you deal with fractional exponents when simplifying radicals?
3. What is the general process for multiplying square roots with variables?
4. How can you factor expressions involving square roots?
5. What are the key rules for handling powers and roots in algebraic expressions?

**Tip:** When multiplying square roots, always try to simplify the numbers and variables inside the square roots first before applying any further operations.

Simplify square root 20w^2 x square root 5wx^2. Assume that all variables represent positive real numbers.

Simplify the expression sqrt(20w^2) * sqrt(5wx^2) step-by-step, covering key algebraic concepts such as radical expressions, multiplication of square roots, and simplification. Suitable for students in Grades 9-11.

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