Questions: Subtract as indicated. Assume all variables are greater than or equal to zero. 3 sqrt(48 x)-3 sqrt(12 x) 3 sqrt(48 x)-3 sqrt(12 x)= (Type an exact answer, using radicals as needed.)

Solution Steps

To solve the expression \(3 \sqrt{48x} - 3 \sqrt{12x}\), we need to simplify each square root term separately. First, factor the numbers inside the square roots to find perfect squares. Then, simplify the square roots and combine like terms.

We start with the expression \(3 \sqrt{48x} - 3 \sqrt{12x}\). We can simplify each square root term separately:

\[ \sqrt{48x} = \sqrt{16 \cdot 3 \cdot x} = \sqrt{16} \cdot \sqrt{3} \cdot \sqrt{x} = 4\sqrt{3x} \]

\[ \sqrt{12x} = \sqrt{4 \cdot 3 \cdot x} = \sqrt{4} \cdot \sqrt{3} \cdot \sqrt{x} = 2\sqrt{3x} \]

Now we substitute the simplified square roots back into the original expression:

\[ 3 \sqrt{48x} - 3 \sqrt{12x} = 3(4\sqrt{3x}) - 3(2\sqrt{3x}) \]

Next, we factor out the common term \(3\sqrt{3x}\):

\[ = 3\sqrt{3x}(4 - 2) = 3\sqrt{3x} \cdot 2 = 6\sqrt{3x} \]

Final Answer