`2(1)/(5) x^(2) = 2750`, find the value of x ?

Options

A. 25
B. `25sqrt(3)`
C. `25sqrt(2)`
D. 20

Answer

To solve the equation \( \frac{2}{5} x^2 = 2750 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{2}{5} x^2 = 2750 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by 5:
\[ 2 x^2 = 2750 \times 5 \]

### Step 3: Calculate the right side
Now, we calculate \( 2750 \times 5 \):
\[ 2750 \times 5 = 13750 \]
So the equation becomes:
\[ 2 x^2 = 13750 \]

### Step 4: Divide by 2
Next, we divide both sides by 2 to isolate \( x^2 \):
\[ x^2 = \frac{13750}{2} \]

### Step 5: Calculate the division
Now, we calculate \( \frac{13750}{2} \):
\[ \frac{13750}{2} = 6875 \]
Thus, we have:
\[ x^2 = 6875 \]

### Step 6: Take the square root
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{6875} \]

### Step 7: Simplify the square root
We can simplify \( \sqrt{6875} \):
\[ 6875 = 25 \times 275 = 25 \times 25 \times 11 = 625 \times 11 \]
Thus:
\[ x = 25 \sqrt{11} \]

### Final Answer
So the value of \( x \) is:
\[ x = 25 \sqrt{11} \]