If `a=1-sqrt(2),"then find the value of "(a-(1)/(a))^(3)`

Explanation

To solve the problem, we need to find the value of \((a - \frac{1}{a})^3\) where \(a = 1 - \sqrt{2}\).

### Step-by-Step Solution:

1. **Substitute the value of \(a\)**:
\[ a = 1 - \sqrt{2} \]

2. **Calculate \(\frac{1}{a}\)**:
To find \(\frac{1}{a}\), we can rationalize the denominator:
\[ \frac{1}{a} = \frac{1}{1 - \sqrt{2}} \cdot \frac{1 + \sqrt{2}}{1 + \sqrt{2}} = \frac{1 + \sqrt{2}}{(1 - \sqrt{2})(1 + \sqrt{2})} \]
The denominator simplifies as follows:
\[ (1 - \sqrt{2})(1 + \sqrt{2}) = 1^2 - (\sqrt{2})^2 = 1 - 2 = -1 \]
Therefore,
\[ \frac{1}{a} = \frac{1 + \sqrt{2}}{-1} = - (1 + \sqrt{2}) = -1 - \sqrt{2} \]

3. **Calculate \(a - \frac{1}{a}\)**:
Now we can find \(a - \frac{1}{a}\):
\[ a - \frac{1}{a} = (1 - \sqrt{2}) - (-1 - \sqrt{2}) = (1 - \sqrt{2}) + (1 + \sqrt{2}) \]
Simplifying this gives:
\[ a - \frac{1}{a} = 1 - \sqrt{2} + 1 + \sqrt{2} = 2 \]

4. **Calculate \((a - \frac{1}{a})^3\)**:
Now we need to find the cube of the result:
\[ (a - \frac{1}{a})^3 = 2^3 = 8 \]

### Final Answer:
The value of \((a - \frac{1}{a})^3\) is \(8\).