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

Question

?(1 point)
Responses

Irrational, because both factors are irrational.
Irrational, because both factors are irrational.

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.

Answer 1

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

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

2. Now substitute this value back into the expression: \[ 512 \cdot \sqrt{16} = 512 \cdot 4 \]

3. Next, perform the multiplication: \[ 512 \cdot 4 = 2048 \]

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

Thus, the correct response is: Rational, because both numbers are rational.