Find the value of `sqrt(11.981+7sqrt(1.2996))`

Options

A. 5.181
B. 3.354
C. 4.467
D. 4.927

Answer

To find the value of \( \sqrt{11.981 + 7\sqrt{1.2996}} \), we can follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{11.981 + 7\sqrt{1.2996}} \]

### Step 2: Calculate \( \sqrt{1.2996} \)
First, we need to find \( \sqrt{1.2996} \). We can express \( 1.2996 \) as:
\[ 1.2996 = \frac{12996}{10000} \]
Thus,
\[ \sqrt{1.2996} = \sqrt{\frac{12996}{10000}} = \frac{\sqrt{12996}}{100} \]

### Step 3: Find \( \sqrt{12996} \)
Now we need to find \( \sqrt{12996} \). We can factor \( 12996 \) to find its square root. After simplifying, we find:
\[ \sqrt{12996} = 114 \]
So,
\[ \sqrt{1.2996} = \frac{114}{100} = 1.14 \]

### Step 4: Substitute back into the expression
Now we substitute \( \sqrt{1.2996} \) back into the original expression:
\[ \sqrt{11.981 + 7 \cdot 1.14} \]

### Step 5: Calculate \( 7 \cdot 1.14 \)
Calculating \( 7 \cdot 1.14 \):
\[ 7 \cdot 1.14 = 7.98 \]

### Step 6: Add \( 11.981 + 7.98 \)
Now we add \( 11.981 + 7.98 \):
\[ 11.981 + 7.98 = 19.961 \]

### Step 7: Take the square root
Finally, we take the square root of \( 19.961 \):
\[ \sqrt{19.961} \approx 4.467 \]

Thus, the value of \( \sqrt{11.981 + 7\sqrt{1.2996}} \) is approximately \( 4.467 \).

### Final Answer:
\[ \sqrt{11.981 + 7\sqrt{1.2996}} \approx 4.467 \]

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