Question

What is the sum and classification of StartFraction 3 Over 20 EndFraction + StartRoot 10 EndRoot?
3.31227766..., irrational
3.31227766..., rational
18.16227766..., irrational
18.16227766..., rational

Answer 1

To find the sum of \(\frac{3}{20} + \sqrt{10}\), let's first calculate the approximate value of each term.

1. **Calculate \(\frac{3}{20}\):**
\[
\frac{3}{20} = 0.15
\]

2. **Calculate \(\sqrt{10}\):**
Approximating \(\sqrt{10}\):
\[
\sqrt{10} \approx 3.16227766
\]

3. **Now, add the two values:**
\[
\frac{3}{20} + \sqrt{10} \approx 0.15 + 3.16227766 \approx 3.31227766
\]

Now, we determine the classification of \(3.31227766...\):

- \(\frac{3}{20}\) is a rational number, while \(\sqrt{10}\) is an irrational number.
- The sum of a rational number and an irrational number is always irrational.

So, the sum is approximately \(3.31227766...\) and it is classified as irrational.

Thus, the correct option is:
**3.31227766..., irrational**.