By rationalising the denominator of each of the following : Find in each case, the value correct to two significant figures :
` (1)/(3-sqrt2) `

Answer

To rationalize the denominator of the expression \( \frac{1}{3 - \sqrt{2}} \) and find its value correct to two significant figures, follow these steps:

### Step 1: Identify the expression
The expression we need to rationalize is:
\[ \frac{1}{3 - \sqrt{2}} \]

### Step 2: Multiply by the conjugate
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator, which is \( 3 + \sqrt{2} \):
\[ \frac{1 \cdot (3 + \sqrt{2})}{(3 - \sqrt{2}) \cdot (3 + \sqrt{2})} \]

### Step 3: Apply the difference of squares formula
Using the difference of squares formula \( (a - b)(a + b) = a^2 - b^2 \), we simplify the denominator:
\[ (3 - \sqrt{2})(3 + \sqrt{2}) = 3^2 - (\sqrt{2})^2 = 9 - 2 = 7 \]

### Step 4: Simplify the numerator
The numerator becomes:
\[ 3 + \sqrt{2} \]

### Step 5: Write the new expression
Now we can write the expression as:
\[ \frac{3 + \sqrt{2}}{7} \]

### Step 6: Substitute the value of \( \sqrt{2} \)
We know that \( \sqrt{2} \approx 1.414 \). Substituting this value in gives:
\[ \frac{3 + 1.414}{7} = \frac{4.414}{7} \]

### Step 7: Perform the division
Now, we divide \( 4.414 \) by \( 7 \):
\[ \frac{4.414}{7} \approx 0.63057142857 \]

### Step 8: Round to two significant figures
Finally, rounding \( 0.63057142857 \) to two significant figures gives:
\[ 0.63 \]

### Final Answer
Thus, the value of \( \frac{1}{3 - \sqrt{2}} \) correct to two significant figures is:
\[ \boxed{0.63} \]