Question

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

an irrational number
an irrational number
an integer
an integer
the number zero
the number zero
a rational number

Answer 1

To determine the type of number resulting from multiplying \(-\sqrt{8}\) and \(45\), we first analyze \(-\sqrt{8}\).

\(\sqrt{8}\) can be simplified:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]
Therefore,
\[
-\sqrt{8} = -2\sqrt{2}
\]

Now, multiply this by \(45\):
\[
-2\sqrt{2} \cdot 45 = -90\sqrt{2}
\]

The number \(\sqrt{2}\) is an irrational number; thus, \(90\sqrt{2}\) is also an irrational number because a rational number (like 90) multiplied by an irrational number (like \(\sqrt{2}\)) remains irrational.

Therefore, the result of multiplying \(-\sqrt{8}\) and \(45\) is an irrational number.

**The correct response is: an irrational number.**