Question

find the sum of $2\sqrt{9}$ and $2\sqrt{16}$ in simplest form. also, determine whether the result is rational or irrational and explain your answer.
answer attempt 1 out of 2
result:
the result is because it be written as the ratio of two integers and its decimal expansion terminate or repeat.

Explanation:

Step1: Simplify \(2\sqrt{9}\)

We know that \(\sqrt{9} = 3\), so \(2\sqrt{9}=2\times3 = 6\).

Step2: Simplify \(2\sqrt{16}\)

We know that \(\sqrt{16}=4\), so \(2\sqrt{16}=2\times4 = 8\).

Step3: Find the sum

Now we add the two results together: \(6 + 8=14\).

Step4: Determine if rational

A rational number is a number that can be written as the ratio of two integers (i.e., a fraction \(\frac{p}{q}\) where \(q
eq0\)). Since \(14=\frac{14}{1}\), and its decimal expansion is \(14.0\) (which is a terminating decimal), it is rational.

Answer:

The sum is \(14\), and it is rational because it can be written as \(\frac{14}{1}\) (the ratio of two integers) and its decimal expansion is terminating.