Question

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

Rational, because both numbers are rational.
Rational, because both numbers are rational. - not selected, this is the correct answer why is this the correct answer?

Irrational, because both factors are irrational.
Irrational, because both factors are irrational. - no response given

Radical, because one factor is a radical.
Radical, because one factor is a radical. - no response given

Irrational, because one factor is irrational.

give me two simple sentences

Answer 1

What type of number will result from
5/12

⋅
√16
?
Responses

Rational, because both numbers are rational.
Rational, because both numbers are rational. - not selected, this is the correct answer

Irrational, because both factors are irrational.
Irrational, because both factors are irrational. - no response given

Radical, because one factor is a radical.
Radical, because one factor is a radical. - no response given

Irrational, because one factor is irrational.

Answer 2

The expression \( 512 \cdot \sqrt{16} \) equals \( 512 \cdot 4 \), which simplifies to 2048. Since both 512 and \( \sqrt{16} \) are rational numbers, their product is also rational.

Answer 3

The expression \( \frac{5}{12} \cdot \sqrt{16} \) simplifies to \( \frac{5}{12} \cdot 4 \), which equals \( \frac{20}{12} \) or \( \frac{5}{3} \). Since both \( \frac{5}{12} \) and \( \sqrt{16} \) (which is 4) are rational numbers, their product is also rational.