If `sqrt ( 0.05 xx 0.5 xx a ) = 0.5 xx 0.0 5 x sqrt b ` then `(a)/(b)` = ?

Options

A. `0.0025`
B. `0.025`
C. `0.25`
D. `2.5`

Answer

To solve the equation \( \sqrt{0.05 \times 0.5 \times a} = 0.5 \times 0.05 \times \sqrt{b} \), we will follow these steps:

### Step 1: Square both sides
We start by squaring both sides of the equation to eliminate the square root.

\[ \left(\sqrt{0.05 \times 0.5 \times a}\right)^2 = \left(0.5 \times 0.05 \times \sqrt{b}\right)^2 \]

### Step 2: Simplify both sides
This simplifies to:

\[ 0.05 \times 0.5 \times a = (0.5 \times 0.05)^2 \times b \]

### Step 3: Calculate \( (0.5 \times 0.05)^2 \)
Now we need to calculate \( (0.5 \times 0.05)^2 \):

\[ 0.5 \times 0.05 = 0.025 \]
\[ (0.025)^2 = 0.000625 \]

### Step 4: Substitute back into the equation
Now we substitute back into our equation:

\[ 0.05 \times 0.5 \times a = 0.000625 \times b \]

### Step 5: Calculate \( 0.05 \times 0.5 \)
Next, we calculate \( 0.05 \times 0.5 \):

\[ 0.05 \times 0.5 = 0.025 \]

### Step 6: Substitute this value
Now we have:

\[ 0.025 \times a = 0.000625 \times b \]

### Step 7: Rearranging the equation
We can rearrange this equation to find \( \frac{a}{b} \):

\[ \frac{a}{b} = \frac{0.000625}{0.025} \]

### Step 8: Calculate \( \frac{0.000625}{0.025} \)
Now we perform the division:

\[ \frac{0.000625}{0.025} = 0.025 \]

### Final Result
Thus, we find:

\[ \frac{a}{b} = 0.025 \]