Question

What is the sum and classification of Two-fifths + StartRoot 88 EndRoot?
9.78083151..., irrational
9.78083151..., rational
13.38083151..., irrational
13.38083151..., rational

Answer 1

To find the sum of \( \frac{2}{5} + \sqrt{88} \), we first compute each part separately.

1. **Calculating \( \sqrt{88} \)**:
\[
\sqrt{88} = \sqrt{4 \times 22} = \sqrt{4} \times \sqrt{22} = 2\sqrt{22}
\]
The value of \( \sqrt{22} \approx 4.690415759 \), thus:
\[
\sqrt{88} \approx 2 \times 4.690415759 \approx 9.380831518
\]

2. **Calculating \( \frac{2}{5} \)**:
\[
\frac{2}{5} = 0.4
\]

3. **Adding the two values**:
\[
\frac{2}{5} + \sqrt{88} = 0.4 + 9.380831518 \approx 9.780831518
\]

4. **Classification**:
The number \( \frac{2}{5} \) is rational, while \( \sqrt{88} \) (which is \( 2\sqrt{22} \)) is irrational. The sum of a rational number and an irrational number is always irrational. Therefore, \( 9.780831518 \) is irrational.

Based on the available options, the correct answer is:
**9.78083151..., irrational.**