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

Question

?(1 point)
Responses

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

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

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

Irrational, because both factors are irrational.

Answer 1

To determine the type of number that results from the expression \(512 \cdot \sqrt{16}\), we first evaluate the square root and then perform the multiplication.

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

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

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

Now, let's analyze the result. The number \(2048\) is a whole number, which is rational (since any integer is a rational number).

Thus, the correct response is:

Rational, because both numbers are rational.