Find the product of 5–√ and 1/6 . What type of number is it?(1 point) Responses 2.40; a rational number 2.40; a rational number 0.3726 . . . ; an irrational number 0.3726 . . . ; an irrational number 0.37; a rational number 0.37; a rational number 2.4027 . . . ; an irrational number

Answer 1

To find the product of \( 5 - \sqrt{5} \) and \( \frac{1}{6} \), let's start with the first term.

1. Calculate \( 5 - \sqrt{5} \):

   • This expression combines a rational number (5) and an irrational number (\( \sqrt{5} \)), which means \( 5 - \sqrt{5} \) is an irrational number.

2. Now we multiply it by \( \frac{1}{6} \):

   • The product is given by \( \left( 5 - \sqrt{5} \right) \left( \frac{1}{6} \right) = \frac{5 - \sqrt{5}}{6} \).

3. This product is still irrational because it is a non-zero rational number divided by an irrational number. The result will always be irrational if the numerator is irrational.

Putting these calculations together, the product \( \frac{5 - \sqrt{5}}{6} \) is an irrational number.

So the correct response is:

0.3726 . . . ; an irrational number