7 * 1 = 64, 3 * 9 = 144
What is the value of 5 * 6 ?

Options

A. 22
B. 55
C. 66
D. 121

Explanation

To solve the problem step by step, we will analyze the given equations and find the pattern to determine the value of \(5 * 6\).

### Step 1: Understand the pattern in the equations
We have two equations:
1. \(7 * 1 = 64\)
2. \(3 * 9 = 144\)

We need to find out how these operations are resulting in the numbers on the right side.

### Step 2: Analyze the first equation
For the first equation \(7 * 1 = 64\):
- If we add the two numbers on the left side: \(7 + 1 = 8\)
- Then, we square the result: \(8^2 = 64\)

### Step 3: Analyze the second equation
For the second equation \(3 * 9 = 144\):
- Add the two numbers on the left side: \(3 + 9 = 12\)
- Square the result: \(12^2 = 144\)

### Step 4: Identify the pattern
From the analysis, we can see that the operation \(x * y\) can be defined as:
\[ x * y = (x + y)^2 \]

### Step 5: Apply the pattern to find \(5 * 6\)
Now, we need to find \(5 * 6\):
- Add the two numbers: \(5 + 6 = 11\)
- Square the result: \(11^2 = 121\)

### Step 6: Conclusion
Thus, the value of \(5 * 6\) is \(121\).

### Final Answer:
The value of \(5 * 6\) is \(121\).

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