Question

1.

What type of number will result from 512⋅16−−√
?

(1 point)
Responses

Irrational because one factor is irrational
Irrational because one factor is irrational

Irrational because both factors are irrational
Irrational because both factors are irrational

Rational because one factor is a radical
Rational because one factor is a radical

Rational because both factors are rational

Answer 1

To evaluate the expression \( 512 \cdot \sqrt{16} \), we first simplify \(\sqrt{16}\):

\[
\sqrt{16} = 4
\]

Now we substitute this value back into the expression:

\[
512 \cdot \sqrt{16} = 512 \cdot 4
\]

Next, we calculate the product:

\[
512 \cdot 4 = 2048
\]

Since \(2048\) is a whole number, it is classified as a rational number.

Thus, the correct response is:

**Rational because one factor is a radical.**