Directions : What approximate value will come in place of the question mark (?) in the following questions? (You are not expected to calculate exact value).
`[(3.0009)^3div(2.999)^4xx(41.998div14.0001)+79.953}^(1/2)`=?

Options

A. 8
B. 9
C. 7
D. 6

Answer

To solve the expression \([(3.0009)^3 \div (2.999)^4 \times (41.998 \div 14.0001) + 79.953]^{1/2}\), we will approximate each component step by step.

### Step 1: Approximate \(3.0009\) and \(2.999\)

- \(3.0009\) can be approximated to \(3\).
- \(2.999\) can be approximated to \(3\).

### Step 2: Calculate \((3.0009)^3\) and \((2.999)^4\)

- \((3.0009)^3 \approx 3^3 = 27\).
- \((2.999)^4 \approx 3^4 = 81\).

### Step 3: Approximate \(41.998\) and \(14.0001\)

- \(41.998\) can be approximated to \(42\).
- \(14.0001\) can be approximated to \(14\).

### Step 4: Calculate \(41.998 \div 14.0001\)

- \(41.998 \div 14.0001 \approx 42 \div 14 = 3\).

### Step 5: Combine the results

Now we can combine the results from steps 2 and 4:

\[ \frac{(3.0009)^3}{(2.999)^4} \times (41.998 \div 14.0001) \approx \frac{27}{81} \times 3 \]

### Step 6: Simplify \(\frac{27}{81}\)

- \(\frac{27}{81} = \frac{1}{3}\).

### Step 7: Calculate \(\frac{1}{3} \times 3\)

- \(\frac{1}{3} \times 3 = 1\).

### Step 8: Approximate \(79.953\)

- \(79.953\) can be approximated to \(80\).

### Step 9: Combine with \(1\)

Now we add \(1\) and \(80\):

\[ 1 + 80 = 81. \]

### Step 10: Calculate the square root

Finally, we take the square root:

\[ \sqrt{81} = 9. \]

### Final Result

The approximate value that comes in place of the question mark (?) is \(9\).

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