Question

What type of number will result from multiplying −8–√
and 45
?(1 point)
Responses

the number zero
the number zero

a rational number
a rational number

an integer
an integer

an irrational number

Answer 1

To determine the type of number that results from multiplying \(-\sqrt{8}\) and \(45\), we first simplify the expression:

\[
-\sqrt{8} \times 45
\]

We can simplify \(\sqrt{8}\):

\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
\]

Now substituting this back into the multiplication:

\[
-\sqrt{8} = -2\sqrt{2}
\]

So now we have:

\[
-2\sqrt{2} \times 45 = -90\sqrt{2}
\]

Now we need to identify the type of the result, \(-90\sqrt{2}\).

- \(\sqrt{2}\) is an irrational number.
- Multiplying a rational number \(-90\) (which is an integer and thus also rational) by an irrational number \(\sqrt{2}\) results in an irrational number.

Thus, the multiplication:

\(-\sqrt{8} \times 45\) yields an **irrational number**.

The correct response is:

**an irrational number.**