Drag and drop the option that would make each statement true.

Question

(2 points)
Put responses in the correct response input area to answer the question.
The product of 3sqrt12 Response input area would yield a rational number.

The product of 3sqrt12 Response input area would yield an irrational number.

Answer 1

To determine whether the product of \( 3\sqrt{12} \) yields a rational or irrational number, we can simplify \( \sqrt{12} \).

1. Simplifying \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

2. Calculating \( 3\sqrt{12} \): \[ 3\sqrt{12} = 3 \cdot 2\sqrt{3} = 6\sqrt{3} \]

Now, since \( \sqrt{3} \) is an irrational number, multiplying it by 6 (a rational number) will still yield an irrational number.

Thus, we can fill in the statements as follows:

• The product of \( 3\sqrt{12} \) would yield a rational number: [This statement is FALSE]
• The product of \( 3\sqrt{12} \) would yield an irrational number: [This statement is TRUE]

Therefore, place "irrational number" in the second response input area and leave the first area empty or write "not true".

Final responses:

1. The product of \( 3\sqrt{12} \) would yield a rational number: [Leave this area empty or write NOT TRUE]
2. The product of \( 3\sqrt{12} \) would yield an irrational number: [Fill with “irrational number”]