`sqrt(25/15625)=sqrt(?/30625)`

Options

A. 2
B. 35
C. 49
D. 1225

Answer

To solve the equation \(\sqrt{\frac{25}{15625}} = \sqrt{\frac{x}{30625}}\), we can follow these steps:

### Step 1: Square both sides
To eliminate the square roots, we square both sides of the equation:

\[ \left(\sqrt{\frac{25}{15625}}\right)^2 = \left(\sqrt{\frac{x}{30625}}\right)^2 \]

This simplifies to:

\[ \frac{25}{15625} = \frac{x}{30625} \]

### Step 2: Cross-multiply
Next, we cross-multiply to solve for \(x\):

\[ 25 \cdot 30625 = x \cdot 15625 \]

### Step 3: Calculate \(25 \cdot 30625\)
Now, we calculate \(25 \cdot 30625\):

\[ 25 \cdot 30625 = 765625 \]

### Step 4: Set up the equation
Now we have:

\[ 765625 = x \cdot 15625 \]

### Step 5: Solve for \(x\)
To find \(x\), we divide both sides by \(15625\):

\[ x = \frac{765625}{15625} \]

### Step 6: Calculate the division
Now we perform the division:

\[ x = 49 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{49} \]

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