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
1 answer
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.
