What type of product will result from multiplying 35

Question

and 3π
?(1 point)
Responses

a fraction
a fraction

a rational number
a rational number

an irrational number
an irrational number

a whole number

Answer 1

To determine the type of product resulting from multiplying \( 35 \) and \( 3\pi \), we can follow these steps:

1. Identify the nature of the numbers:

   • \( 35 \) is a whole number (and also a rational number).
   • \( 3\pi \) involves \( \pi \), which is an irrational number. Therefore, \( 3\pi \) is also irrational.

2. Multiply the numbers:

   • The product \( 35 \times 3\pi = 105\pi \).

3. Determine the nature of the product:

   • The product \( 105\pi \) includes an irrational number (\( \pi \)) multiplied by a rational number (\( 105 \)). The product of a rational number and an irrational number is always an irrational number.

Based on this analysis, the correct response is:

an irrational number.