Answer:
Explanation:
First, we will use the property of radicals that states that (a √b) * (c √d) = (ac) √(bd). Since the expression has both multiplication and addition, we will break the expression down into its components and simplify each component separately.
6√x+7√(54) = 6√x + 7√(27*2) = 6√x + 7√27 * 7√2 = 6√x + 7√27 * (2*√2) = 6√x + 14√27 * √2 .
Next, we will simplify the second component of the expression: 12√(6) = 12√(2*3) = 12√2 * 6√3 = (4*3)√2 * 6√3 = 12√2 * 6√3.
Finally, we can combine the two separate parts of the expression to get the simplified version: 6√x + 14√27 * √2 - 12√2 * 6√3 = 6√x + 14√27 * √2 - 12√6.
The simplified version of the expression is 6√x + 14√27 * √2 - 12√6, in exact terms (no decimals).