Result: [tex]\boldsymbol{20}[/tex]
The result is rational because it can be written as the ratio of two integers and its decimal expansion does terminate or repeat.
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Explanation:
Let's simplify the expression to get...
[tex]2\sqrt{16}+4\sqrt{9}\\\\2\sqrt{4^2}+4\sqrt{3^2}\\\\2*4+4*3\\\\8+12\\\\20\\\\[/tex]
Therefore, [tex]2\sqrt{16}+4\sqrt{9}=20\\\\[/tex]
Since [tex]20 = \frac{20}{1}[/tex], we have a rational number here. It's a fraction of two integers
[tex]\text{rational number} = \frac{\text{integer}}{\text{integer}}[/tex]
We cannot have zero in the denominator.
One property of rational numbers is that the decimal expansion either terminates or it repeats (one option only).
In this case, we have a terminating decimal because 20 = 20.0; ie the decimal doesn't go on forever.
In contrast, something like 1/3 = 0.33333... has the '3's go on forever to be a repeating decimal.
