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 will follow the given information and perform the necessary calculations.

### Step 1: Understand the problem
We are given that the sum of the squares of two numbers is 145. We also know that the square root of one of the numbers is 3.

### Step 2: Define the variables
Let the two numbers be \( x \) and \( y \). According to the problem:
\[ x^2 + y^2 = 145 \]

### Step 3: Find the value of \( x \)
Since the square root of one number is 3, we can find \( x \):
\[ \sqrt{x} = 3 \]
Squaring both sides gives:
\[ x = 3^2 = 9 \]

### Step 4: Substitute \( x \) into the equation
Now we substitute \( x = 9 \) into the equation \( x^2 + y^2 = 145 \):
\[ 9^2 + y^2 = 145 \]
Calculating \( 9^2 \):
\[ 81 + y^2 = 145 \]

### Step 5: Solve for \( y^2 \)
To find \( y^2 \), we rearrange the equation:
\[ y^2 = 145 - 81 \]
Calculating the right side:
\[ y^2 = 64 \]

### Step 6: Find the value of \( y \)
Now, we take the square root of \( y^2 \) to find \( y \):
\[ y = \sqrt{64} = 8 \]

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