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 logic presented in the video transcript.

### Step 1: Identify the given information
We know that:
- The sum of the squares of two numbers is 146.
- The square root of one of the numbers is \( \sqrt{5} \).

### Step 2: Determine the first number
Since the square root of one number is \( \sqrt{5} \), we can find that number by squaring it:
\[ \text{First number} = (\sqrt{5})^2 = 5 \]

### Step 3: Set up the equation for the second number
Let the second number be \( x \). According to the problem, the sum of the squares of both numbers is 146:
\[ 5^2 + x^2 = 146 \]

### Step 4: Calculate the square of the first number
Calculating \( 5^2 \):
\[ 5^2 = 25 \]
So, we can rewrite the equation:
\[ 25 + x^2 = 146 \]

### Step 5: Solve for \( x^2 \)
To find \( x^2 \), we subtract 25 from both sides:
\[ x^2 = 146 - 25 \]
\[ x^2 = 121 \]

### Step 6: Find the value of \( x \)
Now, we take the square root of both sides to find \( x \):
\[ x = \sqrt{121} = 11 \]

### Step 7: Calculate the cube of the second number
Now that we have found \( x \), which is 11, we need to find the cube of this number:
\[ x^3 = 11^3 \]

### Step 8: Compute \( 11^3 \)
Calculating \( 11^3 \):
\[ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 \]

### Final Answer
The cube of the other number is:
\[ \boxed{1331} \]

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