Find the product of 5–√ and 16 . What type of number is it?(1 point) Responses 0.3726 . . . ; an irrational number 0.3726 . . . ; an irrational number 2.4027 . . . ; an irrational number 2.4027 . . . ; an irrational number 2.40; a rational number 2.40; a rational number 0.37; a rational number

Answer 1

To find the product of $5-\sqrt{2}$ and $16$, we calculate:

$$(5-\sqrt{2})\times 16=80-16\sqrt{2}$$

Now, to determine the type of number $80-16\sqrt{2}$ is, we know that $\sqrt{2}$ is an irrational number. Therefore, $16\sqrt{2}$ is also an irrational number. The difference between a rational number (80, which is rational) and an irrational number ($16\sqrt{2}$) is always irrational.

Thus, $80-16\sqrt{2}$ is an irrational number.

Based on the responses provided, the correct response would be:

0.3726 . . . ; an irrational number (noting that this is not the actual value of the product but describes the type).

However, it seems there might be a confusion in the responses you provided since the specific values don't match up. The key takeaway is that $80-16\sqrt{2}$ is indeed an irrational number.