The last two digits of `37^2` is.

Options

A. 69
B. 39
C. 49
D. 79

Answer

To find the last two digits of \( 37^2 \), we can use the identity for the square of a binomial. Here’s a step-by-step solution:

### Step 1: Rewrite the expression
We can express \( 37 \) as \( 40 - 3 \). Therefore, we can rewrite \( 37^2 \) as:
\[ (40 - 3)^2 \]

### Step 2: Apply the binomial square formula
Using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \), where \( a = 40 \) and \( b = 3 \):
\[ (40 - 3)^2 = 40^2 - 2 \cdot 40 \cdot 3 + 3^2 \]

### Step 3: Calculate each term
Now, we calculate each term:
- \( 40^2 = 1600 \)
- \( 2 \cdot 40 \cdot 3 = 240 \)
- \( 3^2 = 9 \)

### Step 4: Combine the results
Substituting these values back into the equation gives us:
\[ 37^2 = 1600 - 240 + 9 \]

### Step 5: Perform the arithmetic
Now, we perform the arithmetic:
\[ 1600 - 240 = 1360 \]
\[ 1360 + 9 = 1369 \]

### Step 6: Find the last two digits
The last two digits of \( 1369 \) are \( 69 \).

### Final Answer
Thus, the last two digits of \( 37^2 \) are \( 69 \).

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