Find the product of V12 and . What type of number is it? (1 point)

Question

• 4.1569
• 2.8867 .
• 4.2974
; an irrational number
an irrational number
; an irrational number
• 2.6307
...; an irrational number

Answer 1

To find the product of \( V12 \) (which is the square root of 12) with the given decimal numbers, we first need to calculate \( V12 \).

Calculating \( V12 \):

\[ V12 = \sqrt{12} \approx 3.4641 \]

Next, let's multiply \( V12 \) with each of the provided numbers and determine the type of number (rational or irrational) that the product represents.

1. With 4.1569: \[ 3.4641 \times 4.1569 \approx 14.4149 \] This product is a rational number.

2. With 2.8867: \[ 3.4641 \times 2.8867 \approx 10.0140 \] This product is a rational number.

3. With 4.2974: \[ 3.4641 \times 4.2974 \approx 14.8970 \] This product is a rational number.

4. With 2.6307: \[ 3.4641 \times 2.6307 \approx 9.1153 \] This product is a rational number.

In all cases, the product of an irrational number (in this case, \( V12 \)) with a rational number (like the decimals you provided) results in an irrational number. Therefore:

Each product \( (V12 \times \text{the decimal number}) \) is an irrational number.