https://file.aiquickdraw.com/mathbot/file/17260166727498z9a4r3m.jpg

The expression you provided is:

\[
\sqrt{4 \cdot \sqrt{6 \cdot \sqrt{36}}}
\]

Let's break it down step-by-step:

### Step 1: Simplify the innermost square root.
\[
\sqrt{36} = 6
\]

Now the expression becomes:
\[
\sqrt{4 \cdot \sqrt{6 \cdot 6}}
\]

### Step 2: Multiply inside the second square root.
\[
6 \cdot 6 = 36
\]

Now the expression is:
\[
\sqrt{4 \cdot \sqrt{36}}
\]

### Step 3: Simplify the second square root.
\[
\sqrt{36} = 6
\]

Now the expression becomes:
\[
\sqrt{4 \cdot 6}
\]

### Step 4: Multiply inside the square root.
\[
4 \cdot 6 = 24
\]

So the expression becomes:
\[
\sqrt{24}
\]

### Step 5: Simplify the square root.
\[
\sqrt{24} = 2\sqrt{6}
\]

Thus, the final simplified result is:
\[
2\sqrt{6}
\]

Let me know if you want further details or have any questions!

---

Here are five related questions you might find helpful:
1. How do you simplify nested square roots?
2. What are the properties of square roots?
3. How do you simplify \(\sqrt{a \cdot b}\)?
4. How do you express a square root in its simplest radical form?
5. How do you handle square roots of perfect squares?

**Tip**: When dealing with nested square roots, always start from the innermost root and work your way outward.

Simplify the expression \(\sqrt{4 \cdot \sqrt{6 \cdot \sqrt{36}}}\)

Learn how to simplify the expression \(\sqrt{4 \cdot \sqrt{6 \cdot \sqrt{36}}}\) with a step-by-step solution. This example demonstrates key algebraic concepts, such as simplifying nested square roots and applying radical expression rules. Ideal for students in Grades 8-10.

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