What approximate value will come in place of question mark (?) in the given questions? (you are not expected to calculate the exact value)
`780+11xxsqrt144.01+59.75=?`

Options

A. 910
B. 500
C. 972
D. 650

Answer

To solve the expression \( 780 + 11 \times \sqrt{144.01} + 59.75 \) and find the approximate value that comes in place of the question mark (?), we can follow these steps:

### Step 1: Approximate the square root
First, we need to approximate \( \sqrt{144.01} \). Since \( 144.01 \) is very close to \( 144 \), we can say:
\[ \sqrt{144.01} \approx \sqrt{144} = 12 \]

**Hint:** When dealing with square roots of numbers close to perfect squares, you can use the perfect square for approximation.

### Step 2: Substitute the approximate value
Now, we substitute the approximate value of the square root back into the expression:
\[ 780 + 11 \times \sqrt{144.01} + 59.75 \approx 780 + 11 \times 12 + 59.75 \]

**Hint:** Always replace the approximated value back into the original expression to continue simplifying.

### Step 3: Calculate the multiplication
Next, we calculate \( 11 \times 12 \):
\[ 11 \times 12 = 132 \]

**Hint:** Multiplication can be done first before adding, simplifying the calculation process.

### Step 4: Add the values together
Now we add all the values together:
\[ 780 + 132 + 59.75 \]

**Hint:** When adding multiple numbers, it can be helpful to group them for easier calculation.

### Step 5: Perform the addition
First, add \( 780 + 132 \):
\[ 780 + 132 = 912 \]
Then add \( 59.75 \):
\[ 912 + 59.75 \approx 971.75 \]

**Hint:** When adding decimals, ensure you align the decimal points for accuracy.

### Step 6: Round to the nearest whole number
Since we are looking for an approximate value, we can round \( 971.75 \) to \( 972 \).

**Hint:** Rounding can help in simplifying the final answer when an exact value isn't necessary.

### Final Answer
Thus, the approximate value that comes in place of the question mark (?) is:
\[ \boxed{972} \]