What approximate value will come in place of the question ,mark (?) in the given questions? (You are not expected to calculate the exact value)
`(39.97xxsqrt?)/55.88=5^2`

Options

A. 625
B. 25
C. 1225
D. 35

Answer

To solve the equation \( \frac{39.97 \times \sqrt{?}}{55.88} = 5^2 \), we will follow these steps:

### Step 1: Simplify the equation
Start by rewriting the equation using approximate values:
\[ \frac{40 \times \sqrt{?}}{56} = 25 \]
Here, we approximate \( 39.97 \) to \( 40 \) and \( 55.88 \) to \( 56 \).

**Hint:** Round the numbers to make calculations easier.

### Step 2: Cross-multiply
Cross-multiply to eliminate the fraction:
\[ 40 \times \sqrt{?} = 25 \times 56 \]

**Hint:** Cross-multiplication helps in simplifying the equation.

### Step 3: Calculate the right side
Calculate \( 25 \times 56 \):
\[ 25 \times 56 = 1400 \]

**Hint:** Break down the multiplication if needed, \( 25 \times 50 + 25 \times 6 \).

### Step 4: Substitute back into the equation
Now substitute back into the equation:
\[ 40 \times \sqrt{?} = 1400 \]

**Hint:** Keep the equation balanced while substituting values.

### Step 5: Isolate \( \sqrt{?} \)
Divide both sides by \( 40 \):
\[ \sqrt{?} = \frac{1400}{40} \]

**Hint:** Simplifying fractions can make calculations easier.

### Step 6: Calculate the division
Calculate \( \frac{1400}{40} \):
\[ \frac{1400}{40} = 35 \]

**Hint:** You can simplify by dividing both the numerator and denominator by 5.

### Step 7: Square both sides
Now square both sides to find \( ? \):
\[ ? = 35^2 \]

**Hint:** Squaring a number gives you the original number multiplied by itself.

### Step 8: Calculate \( 35^2 \)
Calculate \( 35^2 \):
\[ 35^2 = 1225 \]

**Hint:** Remember that \( 35 \times 35 \) can also be calculated as \( (30 + 5)(30 + 5) \).

### Final Answer
The approximate value that will come in place of the question mark (?) is:
\[ \boxed{1225} \]