What is the value of `sqrt(1509+sqrt(144))` ?

Options

A. 39
B. 37
C. 41
D. 49

Answer

To solve the expression \( \sqrt{1509 + \sqrt{144}} \), we can follow these steps:

### Step 1: Simplify \( \sqrt{144} \)
First, we need to find the value of \( \sqrt{144} \).

\[ \sqrt{144} = 12 \]

### Step 2: Substitute the value back into the expression
Now, we substitute \( \sqrt{144} \) back into the original expression:

\[ \sqrt{1509 + \sqrt{144}} = \sqrt{1509 + 12} \]

### Step 3: Add the numbers inside the square root
Next, we add \( 1509 \) and \( 12 \):

\[ 1509 + 12 = 1521 \]

### Step 4: Find \( \sqrt{1521} \)
Now, we need to find the square root of \( 1521 \):

\[ \sqrt{1521} \]

To find this, we can factor \( 1521 \). We can check if it is a perfect square.

### Step 5: Factor \( 1521 \)
We can factor \( 1521 \) as follows:

\[ 1521 = 39 \times 39 = 39^2 \]

### Step 6: Take the square root
Since \( 1521 \) is a perfect square, we can take the square root:

\[ \sqrt{1521} = 39 \]

### Final Answer
Thus, the value of \( \sqrt{1509 + \sqrt{144}} \) is:

\[ \boxed{39} \]