If `a=sqrt((2013)^2+2013+2014)`, then the value of a is

Options

A. 1007
B. 2013
C. 2014
D. 1002

Answer

To solve the problem \( a = \sqrt{(2013)^2 + 2013 + 2014} \), we will follow these steps:

### Step 1: Write down the expression
We start with the expression for \( a \):
\[ a = \sqrt{(2013)^2 + 2013 + 2014} \]

### Step 2: Simplify the expression inside the square root
We can combine the constants \( 2013 \) and \( 2014 \):
\[ 2013 + 2014 = 4027 \]
Thus, we can rewrite the expression as:
\[ a = \sqrt{(2013)^2 + 4027} \]

### Step 3: Calculate \( (2013)^2 \)
Now, we calculate \( (2013)^2 \):
\[ (2013)^2 = 4052169 \]
So, we substitute this value back into the expression:
\[ a = \sqrt{4052169 + 4027} \]

### Step 4: Add the values inside the square root
Next, we add \( 4052169 \) and \( 4027 \):
\[ 4052169 + 4027 = 4056196 \]
Now, we have:
\[ a = \sqrt{4056196} \]

### Step 5: Calculate the square root
Finally, we need to calculate the square root of \( 4056196 \):
\[ a = 2014 \]

### Conclusion
Thus, the value of \( a \) is:
\[ \boxed{2014} \]