Solve for X: Simplifying √8·√4·√2/√2 = √(x²)

To solve this problem, we'll follow these steps:

• Simplify the expression $\sqrt{8}\cdot\sqrt{4}\cdot\sqrt{2}$.
• Divide this product by $\sqrt{2}$.
• Set the result equal to $\sqrt{x^2}$ and solve for $x$.

Now, let's work through each step:

Step 1: First, simplify the product under the square root:

$\sqrt{8}\cdot\sqrt{4}\cdot\sqrt{2} = \sqrt{8\cdot4\cdot2}$.

This simplifies to:

$\sqrt{64}$, because $8 \cdot 4 \cdot 2 = 64$.

Step 2: Now, divide by $\sqrt{2}$:

$\frac{\sqrt{64}}{\sqrt{2}} = \sqrt{\frac{64}{2}} = \sqrt{32}$.

Step 3: Equate this to $\sqrt{x^2}$:

$\sqrt{32} = \sqrt{x^2}$.

This implies $|x| = \sqrt{32}$, giving us two possible solutions: $x = \sqrt{32}$ and $x = -\sqrt{32}$.

Since the simplification naturally leads to positive expressions, we find:

The solution is $x = \sqrt{32}$.