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If x≥ 0 and y > 0 are real numbers, simplify the following expression

The expression in the image appears to be:

\[
\frac{\sqrt{72x}}{6}, \quad x \geq 0
\]

To simplify this:

### Step 1: Simplify the square root
The number inside the square root, 72, can be factored into \(72 = 36 \times 2\), and since 36 is a perfect square, we can simplify it:

\[
\sqrt{72x} = \sqrt{36 \times 2x} = 6\sqrt{2x}
\]

### Step 2: Substitute into the original expression
Now substitute \(6\sqrt{2x}\) into the expression:

\[
\frac{6\sqrt{2x}}{6}
\]

### Step 3: Simplify the expression
The 6's cancel out, so you are left with:

\[
\sqrt{2x}
\]

Thus, the simplified expression is:

\[
\boxed{\sqrt{2x}}
\]

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How do you simplify square roots of non-perfect squares?
2. What is the general process for simplifying radical expressions involving variables?
3. Can you apply this simplification to any other similar expressions involving different numbers?
4. What are the conditions under which the square root function is defined?
5. How does this simplification help in solving equations involving radicals?

**Tip:** Always look for perfect square factors inside the square root to simplify the expression easily.

If x≥ 0 and y > 0 are real numbers, simplify the following expression.

Learn how to simplify the expression involving the square root of 72x with a step-by-step solution. This problem covers key concepts in algebra and simplifying radicals. Suitable for students in Grades 9-11.

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