If `N=sqrt(13+sqrt9)`, then what is the value of `1/N`?

Options

A. `1//2`
B. 2
C. 4
D. `1//4`

Answer

To solve the problem step by step, we start with the expression for \( N \):

### Step 1: Write the expression for \( N \)
Given:
\[ N = \sqrt{13 + \sqrt{9}} \]

### Step 2: Simplify \( \sqrt{9} \)
We know that:
\[ \sqrt{9} = 3 \]
So we can substitute this value into the expression for \( N \):
\[ N = \sqrt{13 + 3} \]

### Step 3: Add the numbers inside the square root
Now, we add \( 13 \) and \( 3 \):
\[ N = \sqrt{16} \]

### Step 4: Calculate the square root of \( 16 \)
We know that:
\[ \sqrt{16} = 4 \]
Thus, we have:
\[ N = 4 \]

### Step 5: Find the value of \( \frac{1}{N} \)
Now we need to find \( \frac{1}{N} \):
\[ \frac{1}{N} = \frac{1}{4} \]

### Final Answer
The value of \( \frac{1}{N} \) is:
\[ \frac{1}{4} \]