Question

What type of number will result from 512
⋅ 16−−√?
?(1 point)
Responses

Radical, because one factor is a radical.
Radical, because one factor is a radical.

Irrational, because one factor is irrational.
Irrational, because one factor is irrational.

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Irrational, because both factors are irrational.

Answer 1

To determine the type of number that results from \( 512 \cdot \sqrt{16} \), we can evaluate the expression step by step:

1. Simplify \( \sqrt{16} \):
\[
\sqrt{16} = 4
\]

2. Now substitute back into the expression:
\[
512 \cdot 4
\]

3. Perform the multiplication:
\[
512 \cdot 4 = 2048
\]

Since both \( 512 \) and \( 4 \) are rational numbers, their product \( 2048 \) is also a rational number.

Therefore, the correct response is:

**Rational, because both numbers are rational.**