Distance of the point ( 3,4,5) from the origin (0,0,0) is

Options

A. `sqrt50`
B. 3
C. 4
D. 5

Explanation

To find the distance of the point (3, 4, 5) from the origin (0, 0, 0), we can use the distance formula in three-dimensional geometry.

### Step-by-Step Solution:

1. **Identify the Coordinates:**
- Let the point \( P \) be \( (x_1, y_1, z_1) = (3, 4, 5) \).
- Let the origin \( O \) be \( (x_2, y_2, z_2) = (0, 0, 0) \).

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

3. **Substituting the Values:**
Substitute the coordinates of points \( P \) and \( O \) into the distance formula:
\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2 + (5 - 0)^2} \]

4. **Calculating Each Term:**
- \( (3 - 0)^2 = 3^2 = 9 \)
- \( (4 - 0)^2 = 4^2 = 16 \)
- \( (5 - 0)^2 = 5^2 = 25 \)

5. **Adding the Squares:**
Now, add these values together:
\[ d = \sqrt{9 + 16 + 25} \]

6. **Calculating the Sum:**
\[ 9 + 16 + 25 = 50 \]

7. **Final Calculation of Distance:**
Therefore, the distance \( d \) is:
\[ d = \sqrt{50} \]

8. **Simplifying the Square Root:**
We can simplify \( \sqrt{50} \):
\[ \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \]

### Final Answer:
The distance of the point (3, 4, 5) from the origin (0, 0, 0) is \( 5\sqrt{2} \) units.

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