What value should come is place of the question mark (?) in the following equation?
`48sqrt(?)+32sqrt(?)=320`

Options

A. 16
B. 2
C. 4
D. 32

Answer

To solve the equation \( 48\sqrt{?} + 32\sqrt{?} = 320 \), we will follow these steps:

### Step 1: Simplify the Equation
Let \( \sqrt{?} = \sqrt{x} \). Then we can rewrite the equation as:
\[ 48\sqrt{x} + 32\sqrt{x} = 320 \]

### Step 2: Combine Like Terms
Now, we can combine the terms on the left side:
\[ (48 + 32)\sqrt{x} = 320 \]
This simplifies to:
\[ 80\sqrt{x} = 320 \]

### Step 3: Isolate \(\sqrt{x}\)
Next, we will isolate \(\sqrt{x}\) by dividing both sides by 80:
\[ \sqrt{x} = \frac{320}{80} \]

### Step 4: Simplify the Right Side
Now, simplify the fraction:
\[ \sqrt{x} = 4 \]

### Step 5: Square Both Sides
To find \(x\), we will square both sides of the equation:
\[ x = 4^2 \]

### Step 6: Calculate \(x\)
Calculating \(4^2\) gives us:
\[ x = 16 \]

Thus, the value that should come in place of the question mark is \( \boxed{16} \).

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