Fill in the blanks with positive integers:

Question

(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)

Answer 1

To fill in the blanks, we need to manipulate the left side of the equation \((3 + \sqrt{6}) \times 3\).

First, we can distribute the 3:

\[ (3 + \sqrt{6}) \times 3 = 3 \times 3 + \sqrt{6} \times 3 = 9 + 3\sqrt{6} \]

Now we can compare this expression \(9 + 3\sqrt{6}\) with the form \(___ + ___ \times \sqrt{6}\).

From this comparison, we see that:

• The first blank should be \(9\).
• The second blank should be \(3\).

Thus, the completed equation is:

\[ (3 + \sqrt{6}) \times 3 = 9 + 3 \times \sqrt{6} \]

Final answer:

\(9\) and \(3\).