What approximate value will come in place of question mark(?) in the given question? (You are not expected to calculate the exact value.)
`(sqrt(25/9) – sqrt(64/81))div sqrt(16/(324))=?`

Options

A. 4.5
B. 2.5
C. 1.5
D. 3.5

Answer

To solve the expression `(sqrt(25/9) – sqrt(64/81)) / sqrt(16/(324))`, we will break it down step by step.

### Step 1: Simplify the square roots
First, we need to simplify each square root in the expression.

1. **Calculate sqrt(25/9)**:
- sqrt(25) = 5
- sqrt(9) = 3
- Therefore, sqrt(25/9) = 5/3.

2. **Calculate sqrt(64/81)**:
- sqrt(64) = 8
- sqrt(81) = 9
- Therefore, sqrt(64/81) = 8/9.

3. **Calculate sqrt(16/324)**:
- sqrt(16) = 4
- sqrt(324) = 18
- Therefore, sqrt(16/324) = 4/18 = 2/9 (after simplifying).

### Step 2: Substitute back into the expression
Now we substitute these simplified values back into the expression:

\[ \frac{(5/3) - (8/9)}{(2/9)} \]

### Step 3: Find a common denominator for the numerator
To subtract the fractions in the numerator, we need a common denominator. The least common multiple of 3 and 9 is 9.

- Convert 5/3 to have a denominator of 9:
- (5/3) = (5 * 3)/(3 * 3) = 15/9.

Now, we can rewrite the numerator:

\[ \frac{15/9 - 8/9}{(2/9)} \]

### Step 4: Simplify the numerator
Now we can subtract the fractions in the numerator:

\[ \frac{(15 - 8)/9}{(2/9)} = \frac{7/9}{(2/9)} \]

### Step 5: Simplify the overall expression
Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{7/9}{(2/9)} = \frac{7}{9} \times \frac{9}{2} = \frac{7}{2} \]

### Step 6: Calculate the approximate value
Now, we need to find the approximate value of 7/2:

\[ \frac{7}{2} = 3.5 \]

Thus, the approximate value that will come in place of the question mark (?) is **3.5**.

### Summary of Steps:
1. Simplify each square root.
2. Substitute simplified values back into the expression.
3. Find a common denominator for the numerator.
4. Simplify the numerator.
5. Simplify the overall expression.
6. Calculate the approximate value.