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What type of number will result from multiplying −8–√

and 4/5
?(1 point)
Responses

a rational number
a rational number

an irrational number
an irrational number

an integer
an integer

the number zero

3 answers

To determine the type of number that results from multiplying \(-8\sqrt{} \) (which seems to be a typographical error and likely means \(-8\sqrt{8}\) or any other number involving a square root) and \(\frac{4}{5}\), we first identify the nature of each component.

Assuming it means \(-8\):

  1. \(-8\) is an integer.
  2. \(\frac{4}{5}\) is a rational number.

Now, multiplying an integer (which is also a rational number) by a rational number results in a rational number.

Thus:

\(-8 \times \frac{4}{5} = -\frac{32}{5}\), which is a rational number.

Given the options:

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

The correct response is:

a rational number.

What type of number will result from multiplying −8√
and 4/5
?(1 point)
Responses

a rational number
a rational number - incorrect

an irrational number
an irrational number - no response given

an integer
an integer - no response given

the number zero

It looks like I misunderstood your initial query regarding the expression \(-8\sqrt{}\). If you meant to write \(-8\sqrt{8}\) or similar, let's clarify the calculation based on different interpretations.

Assuming \(-8\sqrt{8}\):

  1. \(-8\sqrt{8}\) can be rewritten as \(-8 \times 2\sqrt{2} = -16\sqrt{2}\). This number is irrational because \(\sqrt{2}\) is an irrational number, and multiplying it by a non-zero rational number (\(-16\)) gives an irrational result.

Now, let's multiply this by \(\frac{4}{5}\):

\[ -16\sqrt{2} \cdot \frac{4}{5} = -\frac{64\sqrt{2}}{5} \]

This product, \(-\frac{64\sqrt{2}}{5}\), is also irrational because it involves the irrational number \(\sqrt{2}\).

Now, reviewing your response options:

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

Given the interpretation that involves \(-8\sqrt{8}\) or any other square root that keeps \(\sqrt{2}\) in the expression, the correct option here would be:

an irrational number.

If you'd like to clarify what \(-8\sqrt{}\) was meant to represent specifically, I can provide a more accurate assessment based on that.