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. The distance \( D \) between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) is given by the formula:

\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

### Step 1: Identify the coordinates
Here, we have:
- Point \( A(0, 0, 0) \) (the origin)
- Point \( B(3, 4, 5) \)

### Step 2: Substitute the coordinates into the formula
Using the distance formula, we substitute the coordinates:
- \( x_1 = 0, y_1 = 0, z_1 = 0 \)
- \( x_2 = 3, y_2 = 4, z_2 = 5 \)

The formula becomes:

\[ D = \sqrt{(3 - 0)^2 + (4 - 0)^2 + (5 - 0)^2} \]

### Step 3: Calculate the differences
Calculating the differences gives us:

\[ D = \sqrt{3^2 + 4^2 + 5^2} \]

### Step 4: Calculate the squares
Now, we calculate the squares of the differences:

\[ D = \sqrt{9 + 16 + 25} \]

### Step 5: Add the squared values
Adding these values together:

\[ D = \sqrt{50} \]

### Step 6: Simplify the square root
We can simplify \( \sqrt{50} \):

\[ D = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Final Answer
Thus, the distance of the point \( (3, 4, 5) \) from the origin \( (0, 0, 0) \) is:

\[ \boxed{5\sqrt{2}} \]