Find the distance between origin and (2, 5, 6).

Answer

To find the distance between the origin (0, 0, 0) and the point (2, 5, 6), we will use the distance formula in three-dimensional geometry.

### Step-by-Step Solution:

1. **Identify the Points**:
- Origin (O) = (0, 0, 0)
- Point P = (2, 5, 6)

2. **Distance Formula**:
The distance \( d \) between two points \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \) in three-dimensional space is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

3. **Substituting the Values**:
Here, we can denote:
- \( x_1 = 0, y_1 = 0, z_1 = 0 \) (coordinates of the origin)
- \( x_2 = 2, y_2 = 5, z_2 = 6 \) (coordinates of point P)

Now substituting these values into the distance formula:
\[ d = \sqrt{(2 - 0)^2 + (5 - 0)^2 + (6 - 0)^2} \]

4. **Calculating Each Term**:
- \( (2 - 0)^2 = 2^2 = 4 \)
- \( (5 - 0)^2 = 5^2 = 25 \)
- \( (6 - 0)^2 = 6^2 = 36 \)

5. **Adding the Squares**:
Now we add these values together:
\[ d = \sqrt{4 + 25 + 36} \]

6. **Final Calculation**:
\[ d = \sqrt{65} \]

Thus, the distance between the origin and the point (2, 5, 6) is \( \sqrt{65} \).