If `sqrt(2)= 1.4 ` and `sqrt(3)` = 1.7 find the value of each of the correct to one decimal place:
`(1)/(3+2sqrt(2))`

Answer

To solve the problem of finding the value of \( \frac{1}{3 + 2\sqrt{2}} \) using the approximations \( \sqrt{2} = 1.4 \) and \( \sqrt{3} = 1.7 \), we can follow these steps:

### Step 1: Substitute the value of \( \sqrt{2} \)
We start by substituting the value of \( \sqrt{2} \) into the expression:
\[ 3 + 2\sqrt{2} = 3 + 2 \times 1.4 \]

### Step 2: Calculate \( 2\sqrt{2} \)
Now, calculate \( 2 \times 1.4 \):
\[ 2 \times 1.4 = 2.8 \]

### Step 3: Add to 3
Next, we add this result to 3:
\[ 3 + 2.8 = 5.8 \]

### Step 4: Find the reciprocal
Now, we need to find the reciprocal of \( 5.8 \):
\[ \frac{1}{5.8} \]

### Step 5: Calculate \( \frac{1}{5.8} \)
To calculate \( \frac{1}{5.8} \), we can use a calculator or perform long division. The approximate value is:
\[ \frac{1}{5.8} \approx 0.1724 \]

### Step 6: Round to one decimal place
Finally, rounding \( 0.1724 \) to one decimal place gives us:
\[ 0.2 \]

### Final Answer
Thus, the value of \( \frac{1}{3 + 2\sqrt{2}} \) correct to one decimal place is:
\[ \boxed{0.2} \]