Sum of squares of two numbers is 145. If square root of one number is 3, the other number is equal to:

Options

A. 136
B. 64
C. 9
D. 8

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the problem
We need to find two numbers whose squares sum up to 145. We know that the square root of one of the numbers is 3.

### Step 2: Define the variables
Let:
- \( x \) be the first number
- \( y \) be the second number

### Step 3: Set up the equations
From the problem, we have two key pieces of information:
1. The sum of the squares of the two numbers is 145:
\[ x^2 + y^2 = 145 \quad \text{(Equation 1)} \]
2. The square root of one number is 3, which means:
\[ x = 3^2 = 9 \]

### Step 4: Substitute the value of \( x \) into Equation 1
Now, substitute \( x = 9 \) into Equation 1:
\[ 9^2 + y^2 = 145 \]

### Step 5: Calculate \( 9^2 \)
Calculate \( 9^2 \):
\[ 81 + y^2 = 145 \]

### Step 6: Isolate \( y^2 \)
Now, isolate \( y^2 \) by subtracting 81 from both sides:
\[ y^2 = 145 - 81 \]
\[ y^2 = 64 \]

### Step 7: Solve for \( y \)
Now, take the square root of both sides to find \( y \):
\[ y = \sqrt{64} = 8 \]

### Conclusion
The other number is \( y = 8 \).