Question

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

a rational number 
a rational number 

an integer
an integer

an irrational number 
an irrational number 

the number zero

Answer 1

To analyze the multiplication of \(-8\sqrt{}\) (which seems to have a missing number under the square root) and \(45\), let's first clarify what type of number we're dealing with.

If we assume you meant \(-8\sqrt{c}\) for some positive number \(c\), then:

1. **Determine the nature of \(\sqrt{c}\)**:
- If \(c\) is a positive real number, \(\sqrt{c}\) is an irrational number unless \(c\) is a perfect square.

2. **Multiply that by \(45\)**:
- If \(c\) is not a perfect square, then \(\sqrt{c}\) is irrational.
- The product of a rational number (like \(45\)) and an irrational number (like \(\sqrt{c}\)) is always irrational.

3. **Evaluate the options**:
- If \(c\) is a perfect square, \(\sqrt{c}\) becomes rational. Thus, \(-8\sqrt{c}\) is rational and \(-8\sqrt{c} \times 45\) remains rational.

So without more information about \(c\), we have two possibilities:

- If \(c\) is a perfect square, the answer is **a rational number**.
- If \(c\) is not a perfect square, the answer is **an irrational number**.

Since there's ambiguity without knowing the actual square root, if \(c\) isn't specified and typically among mathematical questions like these, the assumption might lean toward that \(\sqrt{c}\) being irrational if unspecified.

In conclusion:

If \(-8\sqrt{c}\) is interpreted as \(-8\) times the square root of a number that is not a perfect square, the answer would be **an irrational number**. If \(c\) were to denote a perfect square, it would be **a rational number**.

Typically, the wrong delineation about deeper solutions points at the potential complexity likely leaning toward the irrational scenario.

So the best immediate guess would be: **an irrational number**, unless more information clarifies the type of \(c\).