The value of `sqrt(40+sqrt(9sqrt(81)))` is

Options

A. `sqrt(111)`
B. `9`
C. `7`
D. `11`

Answer

To solve the expression \( \sqrt{40 + \sqrt{9\sqrt{81}}} \), we will break it down step by step.

### Step 1: Simplify the inner square root
First, we simplify \( \sqrt{9\sqrt{81}} \).

- We know that \( \sqrt{81} = 9 \).
- Therefore, \( \sqrt{9\sqrt{81}} = \sqrt{9 \times 9} = \sqrt{81} = 9 \).

### Step 2: Substitute back into the original expression
Now we can substitute this back into the original expression:

\[ \sqrt{40 + \sqrt{9\sqrt{81}}} = \sqrt{40 + 9} \]

### Step 3: Add the numbers inside the square root
Next, we add the numbers inside the square root:

\[ 40 + 9 = 49 \]

### Step 4: Take the square root
Now we take the square root of 49:

\[ \sqrt{49} = 7 \]

### Final Answer
Thus, the value of \( \sqrt{40 + \sqrt{9\sqrt{81}}} \) is \( 7 \).

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