Question

Simplify 2√7x * 3√14x^2

Answer 1

`2√(7x) \cdot 3√(14x^2)`

• Set up

`6√(98x^3)`

• Combine terms through multiplying

`6 √(49 \cdot 2 \cdot x^2 \cdot x) = 6√(49x^2 \cdot 2x)`

• 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
  `x^3` into
  `x^2` (a square) and
  `x`.

`6√(49x^2) \cdot √(2x)`

• Split up the square root to isolate the perfect square

`6 \cdot 7x \cdot √(2x)`

• Simplify the square root

`42x√(2x)`

• Simplify the entire expression through multiplying

The simplified form is
`\boxed{42x √(2x)}`.