If `a = sqrt((2016)^(2) + (2016) + 2017)`, then the value of a is

Options

A. 2017
B. 2016
C. 2018
D. 2019

Answer

To solve the problem, we need to simplify the expression given for \( a \):

\[ a = \sqrt{(2016)^2 + (2016) + 2017} \]

### Step 1: Rewrite the expression inside the square root
We start with the expression:

\[ a = \sqrt{2016^2 + 2016 + 2017} \]

We can combine the last two terms:

\[ a = \sqrt{2016^2 + 2016 + 1 + 2016} \]

### Step 2: Group the terms
Now we can group the terms as follows:

\[ a = \sqrt{2016^2 + 2 \cdot 2016 + 1} \]

### Step 3: Recognize the perfect square
Notice that the expression \( 2016^2 + 2 \cdot 2016 + 1 \) can be recognized as a perfect square:

\[ a = \sqrt{(2016 + 1)^2} \]

### Step 4: Simplify the square root
Since we have a square root of a square, we can simplify it:

\[ a = 2016 + 1 \]

### Step 5: Calculate the final value
Now we can calculate the final value:

\[ a = 2017 \]

Thus, the value of \( a \) is:

\[ \boxed{2017} \]

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