The value of `sqrt(91 + sqrt(70+ sqrt(121)))` is

Options

A. 10
B. 11
C. 12
D. 9

Answer

To solve the expression \( \sqrt{91 + \sqrt{70 + \sqrt{121}}} \), we will follow these steps:

### Step 1: Simplify the innermost square root
First, we simplify \( \sqrt{121} \):
\[ \sqrt{121} = 11 \]

### Step 2: Substitute back into the expression
Now, substitute \( \sqrt{121} \) back into the expression:
\[ \sqrt{70 + \sqrt{121}} = \sqrt{70 + 11} = \sqrt{81} \]

### Step 3: Simplify the square root
Next, simplify \( \sqrt{81} \):
\[ \sqrt{81} = 9 \]

### Step 4: Substitute back into the outer expression
Now, substitute \( \sqrt{81} \) back into the outer expression:
\[ \sqrt{91 + \sqrt{70 + \sqrt{121}}} = \sqrt{91 + 9} = \sqrt{100} \]

### Step 5: Simplify the final square root
Finally, simplify \( \sqrt{100} \):
\[ \sqrt{100} = 10 \]

Thus, the value of \( \sqrt{91 + \sqrt{70 + \sqrt{121}}} \) is \( 10 \).

### Final Answer:
\[ \text{The value is } 10. \]

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