Find the value of (?) in following approximation questions: `(339.99)/? = sqrt(143.99)+sqrt(64.01)`

Options

A. 19
B. 17
C. 12
D. 23

Answer

To solve the equation \( \frac{339.99}{?} = \sqrt{143.99} + \sqrt{64.01} \), we will follow these steps:

### Step 1: Approximate the square roots
First, we need to approximate the values of \( \sqrt{143.99} \) and \( \sqrt{64.01} \).

- For \( \sqrt{143.99} \):
- The nearest perfect square is \( 144 \), and \( \sqrt{144} = 12 \).
- Since \( 143.99 \) is very close to \( 144 \), we can approximate \( \sqrt{143.99} \approx 12 \).

- For \( \sqrt{64.01} \):
- The nearest perfect square is \( 64 \), and \( \sqrt{64} = 8 \).
- Since \( 64.01 \) is very close to \( 64 \), we can approximate \( \sqrt{64.01} \approx 8 \).

### Step 2: Add the approximated square roots
Now, we add the two approximated values:
\[ \sqrt{143.99} + \sqrt{64.01} \approx 12 + 8 = 20 \]

### Step 3: Set up the equation
Now we can set up the equation based on our approximation:
\[ \frac{339.99}{?} = 20 \]

### Step 4: Solve for ?
To find the value of \( ? \), we can rearrange the equation:
\[ ? = \frac{339.99}{20} \]

### Step 5: Calculate the value
Now, we perform the division:
\[ ? = \frac{339.99}{20} \approx 17 \]

### Conclusion
Thus, the value of \( ? \) is approximately \( 17 \).

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