Directions : What approximate value will come in place of the question mark (?) in the following questions? (You are not expected to calculate exact value).
`342^(2/3)+sqrt(?-40.05)=64.83`

Options

A. 225
B. 192
C. 136
D. 296

Answer

To solve the equation \( 342^{(2/3)} + \sqrt{? - 40.05} = 64.83 \), we will follow these steps:

### Step 1: Approximate \( 342^{(2/3)} \)
First, we can approximate \( 342 \) to \( 343 \) since it is close to a perfect cube.

\[ 343^{(2/3)} = (7^3)^{(2/3)} = 7^2 = 49 \]

### Step 2: Substitute the approximation into the equation
Now we substitute this approximation back into the equation:

\[ 49 + \sqrt{? - 40.05} \approx 64.83 \]

### Step 3: Isolate the square root term
Next, we isolate the square root term:

\[ \sqrt{? - 40.05} \approx 64.83 - 49 \]
\[ \sqrt{? - 40.05} \approx 15.83 \]

### Step 4: Square both sides
Now, we square both sides to eliminate the square root:

\[ ? - 40.05 \approx (15.83)^2 \]

Calculating \( (15.83)^2 \):

\[ (15.83)^2 \approx 250.51 \]

### Step 5: Solve for ?
Now we can solve for \( ? \):

\[ ? \approx 250.51 + 40.05 \]
\[ ? \approx 290.56 \]

### Step 6: Round to the nearest option
Since we are looking for an approximate value, we can round \( 290.56 \) to \( 296 \), which is one of the options provided.

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

\[ \boxed{296} \]

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