The product of two numbers is 48. The sum of their squares is 100. Sum of these two numbers is equal to:

Options

A. 14
B. 16
C. 19
D. 24

Answer

To solve the problem, we need to find the sum of two numbers \( x \) and \( y \) given the following conditions:

1. The product of the two numbers is 48:
\[ xy = 48 \]

2. The sum of their squares is 100:
\[ x^2 + y^2 = 100 \]

We want to find the sum \( x + y \).

### Step 1: Use the identity for the sum of squares
We can use the identity that relates the sum of squares to the sum and product of the numbers:
\[ x^2 + y^2 = (x + y)^2 - 2xy \]

### Step 2: Substitute the known values
From the conditions, we know:
- \( xy = 48 \)
- \( x^2 + y^2 = 100 \)

Substituting these into the identity:
\[ 100 = (x + y)^2 - 2(48) \]

### Step 3: Simplify the equation
This simplifies to:
\[ 100 = (x + y)^2 - 96 \]
\[ 100 + 96 = (x + y)^2 \]
\[ 196 = (x + y)^2 \]

### Step 4: Take the square root
Now, we take the square root of both sides:
\[ x + y = \sqrt{196} \]
\[ x + y = 14 \]

### Conclusion
Thus, the sum of the two numbers is:
\[ \boxed{14} \]