Question

Question

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

(2 points)
Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The product of 312−−√
and Press enter key to drop response here.Response input area would yield a rational number.

The product of 312−−√
and Press enter key to drop response here.Response input area would yield an irrational number.

Answer 1

To make each statement true, we first need to identify the nature of the number \( \sqrt{312} \).

1. The product of \( \sqrt{312} \) and a rational number would yield a rational number.

   • Response for this statement: Any rational number, such as \( 1 \) or any integer like \( 2 \).

2. The product of \( \sqrt{312} \) and an irrational number would yield an irrational number.

   • Response for this statement: Any irrational number, such as \( \sqrt{2} \) or \( \pi \).

To summarize for your drag-and-drop task:

• For the first statement, drop a rational number (e.g., \( 1 \) or \( 2 \)).
• For the second statement, drop an irrational number (e.g., \( \sqrt{2} \) or \( \pi \)).