The value of `sqrt(91+(sqrt(70+sqrt121))` is

Options

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

Answer

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

### Step 1: Simplify \( \sqrt{121} \)
First, we need to calculate \( \sqrt{121} \):
\[ \sqrt{121} = 11 \]

### Step 2: Substitute \( \sqrt{121} \) into the expression
Now, substitute \( 11 \) back into the expression:
\[ \sqrt{91 + \sqrt{70 + 11}} \]

### Step 3: Simplify \( 70 + 11 \)
Next, we simplify \( 70 + 11 \):
\[ 70 + 11 = 81 \]

### Step 4: Substitute \( 81 \) into the expression
Now, substitute \( 81 \) back into the expression:
\[ \sqrt{91 + \sqrt{81}} \]

### Step 5: Simplify \( \sqrt{81} \)
Now, calculate \( \sqrt{81} \):
\[ \sqrt{81} = 9 \]

### Step 6: Substitute \( 9 \) into the expression
Now, substitute \( 9 \) back into the expression:
\[ \sqrt{91 + 9} \]

### Step 7: Simplify \( 91 + 9 \)
Now, simplify \( 91 + 9 \):
\[ 91 + 9 = 100 \]

### Step 8: Calculate \( \sqrt{100} \)
Finally, calculate \( \sqrt{100} \):
\[ \sqrt{100} = 10 \]

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

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