The sum of the squares of 2 numbers is 146 and the square root of one of them is `sqrt(5)`. The cube of the other number is

Options

A. 1111
B. 1221
C. 1331
D. 1441

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Variables
Let the two numbers be \( x \) and \( y \). According to the problem, the sum of the squares of these two numbers is given as:
\[ x^2 + y^2 = 146 \]

### Step 2: Use the Given Information
We know that the square root of one of the numbers is \( \sqrt{5} \). We can assume \( x = \sqrt{5} \). Therefore, we can find \( x^2 \):
\[ x^2 = (\sqrt{5})^2 = 5 \]

### Step 3: Substitute \( x^2 \) in the Equation
Now, we substitute \( x^2 \) into the equation from Step 1:
\[ 5 + y^2 = 146 \]

### Step 4: Solve for \( y^2 \)
To find \( y^2 \), we subtract 5 from both sides:
\[ y^2 = 146 - 5 = 141 \]

### Step 5: Find \( y \)
Now, we take the square root of \( y^2 \) to find \( y \):
\[ y = \sqrt{141} \]

### Step 6: Calculate the Cube of \( y \)
We need to find the cube of the other number \( y \):
\[ y^3 = (\sqrt{141})^3 \]
This can be simplified as:
\[ y^3 = \sqrt{141} \times 141 = 141\sqrt{141} \]

### Step 7: Final Calculation
To find the numerical value of \( y^3 \), we can compute:
\[ y^3 = 141 \times \sqrt{141} \]
However, since the problem asks for the cube of the other number, we can also express it as:
\[ y^3 = 141^{3/2} \]

### Final Answer
Thus, the cube of the other number \( y \) is:
\[ y^3 = 141\sqrt{141} \]