[tex]2\sqrt{7x} \cdot 3\sqrt{14x^2}[/tex]
[tex]6\sqrt{98x^3}[/tex]
- Combine terms through multiplying
[tex]6 \sqrt{49 \cdot 2 \cdot x^2 \cdot x} = 6\sqrt{49x^2 \cdot 2x}[/tex]
- Order the terms under the square root to find perfect squares. In this case, we can split 98 into 49 (a square) and 2. We can also split [tex]x^3[/tex] into [tex]x^2[/tex] (a square) and [tex]x[/tex].
[tex]6\sqrt{49x^2} \cdot \sqrt{2x}[/tex]
- Split up the square root to isolate the perfect square
[tex]6 \cdot 7x \cdot \sqrt{2x}[/tex]
[tex]42x\sqrt{2x}[/tex]
- Simplify the entire expression through multiplying
The simplified form is [tex]\boxed{42x \sqrt{2x}}[/tex].
