Calculate the value of `root3(64)+sqrt(9^(2))`

Options

A. 4
B. 3
C. 13
D. 77

Answer

To solve the expression \( \sqrt[3]{64} + \sqrt{9^2} \), we will break it down into two parts: the cube root of 64 and the square root of \( 9^2 \).

### Step-by-step Solution:

1. **Calculate the Cube Root of 64:**
- The cube root of a number \( x \) is the number \( y \) such that \( y^3 = x \).
- Here, we need to find \( \sqrt[3]{64} \).
- We know that \( 4 \times 4 \times 4 = 64 \) (since \( 4^3 = 64 \)).
- Therefore, \( \sqrt[3]{64} = 4 \).

2. **Calculate the Square Root of \( 9^2 \):**
- The square root of a number \( x \) is the number \( y \) such that \( y^2 = x \).
- Here, we need to find \( \sqrt{9^2} \).
- We know that \( 9^2 = 81 \).
- Thus, \( \sqrt{9^2} = \sqrt{81} = 9 \).

3. **Add the Results:**
- Now we combine the results from the two calculations:
- \( \sqrt[3]{64} + \sqrt{9^2} = 4 + 9 = 13 \).

### Final Answer:
The value of \( \sqrt[3]{64} + \sqrt{9^2} \) is \( 13 \).