Given that `sqrt(3)=1.732` and `sqrt(5)=2.236` then find the value of `((6)/(sqrt(5)-sqrt(3)))` .

Answer

To solve the problem \( \frac{6}{\sqrt{5} - \sqrt{3}} \) using the given values \( \sqrt{3} = 1.732 \) and \( \sqrt{5} = 2.236 \), we can follow these steps:

### Step 1: Substitute the values of the square roots
We start by substituting the values of \( \sqrt{5} \) and \( \sqrt{3} \) into the expression.

\[ \sqrt{5} = 2.236 \quad \text{and} \quad \sqrt{3} = 1.732 \]

So, we have:
\[ \frac{6}{\sqrt{5} - \sqrt{3}} = \frac{6}{2.236 - 1.732} \]

### Step 2: Calculate the denominator
Now, we need to calculate the denominator \( 2.236 - 1.732 \).

\[ 2.236 - 1.732 = 0.504 \]

### Step 3: Substitute the calculated denominator back into the expression
Now we substitute back into the expression:

\[ \frac{6}{0.504} \]

### Step 4: Perform the division
Now we perform the division:

\[ \frac{6}{0.504} = 11.90476190 \ldots \]

### Step 5: Round the answer
For practical purposes, we can round the answer to a reasonable number of decimal places. Thus, we can say:

\[ \frac{6}{\sqrt{5} - \sqrt{3}} \approx 11.90 \]

### Final Answer
The final answer is approximately \( 11.90 \).

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