If `sqrt(2)=1. 4142 ,` then `sqrt((sqrt(2)-1)/(sqrt(2)+1))` is equal to

Options

A. 2. 4142……
B. 5.8282……
C. 0.4142…….
D. 0.1718……

Answer

To solve the problem, we need to evaluate the expression:

\[ \sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} \]

Given that \(\sqrt{2} = 1.4142\), we can follow these steps:

### Step 1: Substitute the value of \(\sqrt{2}\)

Substituting \(\sqrt{2}\) with \(1.4142\):

\[ \sqrt{\frac{1.4142 - 1}{1.4142 + 1}} \]

### Step 2: Simplify the numerator and denominator

Calculating the numerator:

\[ 1.4142 - 1 = 0.4142 \]

Calculating the denominator:

\[ 1.4142 + 1 = 2.4142 \]

So, we have:

\[ \sqrt{\frac{0.4142}{2.4142}} \]

### Step 3: Simplify the fraction

Now we simplify the fraction:

\[ \frac{0.4142}{2.4142} \]

This can be approximated as:

\[ \approx 0.171 \]

### Step 4: Take the square root

Now we take the square root of \(0.171\):

\[ \sqrt{0.171} \approx 0.4142 \]

### Step 5: Final result

Thus, we have:

\[ \sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} \approx 0.4142 \]

### Conclusion

The final result is:

\[ \sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} = \sqrt{2} - 1 \approx 0.4142 \]