Sure, let's solve this problem step-by-step!
1. Calculate the square root of 16:
[tex]\[
\sqrt{16}
\][/tex]
The square root of 16 is 4 because [tex]\(4 \times 4 = 16\)[/tex].
So,
[tex]\[
\sqrt{16} = 4
\][/tex]
2. Multiply the square root by 3:
[tex]\[
4 \cdot 3
\][/tex]
When you multiply 4 by 3, you get 12.
Therefore,
[tex]\[
4 \cdot 3 = 12
\][/tex]
3. Determine if the result is a rational or irrational number:
- A rational number is any number that can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex] of two integers, where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex].
- An irrational number is a number that cannot be expressed as a simple fraction.
In this case:
[tex]\[
12 = \frac{12}{1}
\][/tex]
Since 12 can be expressed as the quotient of two integers (12 and 1), it is a rational number.
Therefore, the result of [tex]\(\sqrt{16} \cdot 3\)[/tex] is:
[tex]\[
12
\][/tex]
And [tex]\(12\)[/tex] is a rational number.
