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.