Simplify `(sqrt(25.4016) - sqrt(1.0609))/(sqrt(25.4016) + sqrt(1.0609))` :

Options

A. `401/607`
B. `104/706`
C. `41//76`
D. None of these

Answer

To simplify the expression \((\sqrt{25.4016} - \sqrt{1.0609}) / (\sqrt{25.4016} + \sqrt{1.0609})\), we will follow these steps:

### Step 1: Calculate the square roots
First, we need to find the square roots of the numbers in the expression.

- \(\sqrt{25.4016} = 5.04\)
- \(\sqrt{1.0609} = 1.03\)

### Step 2: Substitute the square roots back into the expression
Now, we substitute the calculated square roots back into the original expression:

\[ \frac{\sqrt{25.4016} - \sqrt{1.0609}}{\sqrt{25.4016} + \sqrt{1.0609}} = \frac{5.04 - 1.03}{5.04 + 1.03} \]

### Step 3: Simplify the numerator and denominator
Next, we simplify both the numerator and the denominator:

- Numerator: \(5.04 - 1.03 = 4.01\)
- Denominator: \(5.04 + 1.03 = 6.07\)

So, the expression now looks like this:

\[ \frac{4.01}{6.07} \]

### Step 4: Simplify the fraction
Now, we can simplify the fraction \(\frac{4.01}{6.07}\):

To do this, we can divide both the numerator and the denominator by 4.01:

\[ \frac{4.01 \div 4.01}{6.07 \div 4.01} = \frac{1}{\frac{6.07}{4.01}} \approx \frac{1}{1.51} \]

### Final Result
Thus, the simplified expression is approximately:

\[ \frac{1}{1.51} \approx 0.6623 \]