Question

What type of number will result from multiplying negative square root 8 and 4/5?

Answer 1

To find the result of multiplying \(-\sqrt{8}\) and \(\frac{4}{5}\), let's first simplify \(-\sqrt{8}\):

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

Now, multiply this result by \(\frac{4}{5}\):

\[
-\sqrt{8} \times \frac{4}{5} = -2\sqrt{2} \times \frac{4}{5} = -\frac{8\sqrt{2}}{5}
\]

Now, we analyze the type of number we have:

1. **The value of \(-\frac{8\sqrt{2}}{5}\)**:
- \(\sqrt{2}\) is an irrational number.
- Multiplying an irrational number by a rational number (in this case, \(-\frac{8}{5}\)) results in an irrational number.

Thus, the final result of multiplying \(-\sqrt{8}\) and \(\frac{4}{5}\) is an **irrational number**.