What approximate value will come in place of the question mark(?) in the given questions? (You are not expected to calculate exact value)
`179.92-sqrt(218.08)-?=19.97`

Options

A. 129
B. 137
C. 144
D. 121

Answer

To solve the equation \( 179.92 - \sqrt{218.08} - ? = 19.97 \), we will follow these steps:

### Step 1: Simplify the equation
We can rearrange the equation to isolate the question mark (?):
\[ ? = 179.92 - \sqrt{218.08} - 19.97 \]

### Step 2: Approximate the values
We will approximate \( 179.92 \) to \( 180 \) for simplicity.

### Step 3: Estimate \( \sqrt{218.08} \)
To estimate \( \sqrt{218.08} \), we can find two perfect squares it lies between. We know:
- \( \sqrt{196} = 14 \) (since \( 14^2 = 196 \))
- \( \sqrt{225} = 15 \) (since \( 15^2 = 225 \))

Since \( 218.08 \) is closer to \( 225 \) than \( 196 \), we can approximate \( \sqrt{218.08} \) to be around \( 15 \).

### Step 4: Substitute the approximated values back into the equation
Now substituting the approximated values into the equation:
\[ ? \approx 180 - 15 - 19.97 \]

### Step 5: Simplify further
Calculating the right-hand side:
\[ ? \approx 180 - 15 - 20 \approx 180 - 35 = 145 \]

### Step 6: Conclusion
The approximate value of \( ? \) is \( 145 \). Among the options provided, the closest value is \( 144 \).

Thus, the answer is:
\[ \text{Option 3: } 144 \]

---