Evaluate:
` sqrt(4(73)/(324))`

Answer

To evaluate the expression \( \sqrt{\frac{4 \times 73}{324}} \), we will follow these steps:

### Step 1: Simplify the expression inside the square root
We start with the expression:
\[ \sqrt{\frac{4 \times 73}{324}} \]
Calculating the numerator:
\[ 4 \times 73 = 292 \]
So, we rewrite the expression as:
\[ \sqrt{\frac{292}{324}} \]

### Step 2: Simplify the fraction
Next, we simplify \( \frac{292}{324} \). We can find the greatest common divisor (GCD) of 292 and 324.

The prime factorization of 292:
- \( 292 = 4 \times 73 = 2^2 \times 73 \)

The prime factorization of 324:
- \( 324 = 18 \times 18 = 2^2 \times 3^4 \)

The GCD of 292 and 324 is \( 4 \) (or \( 2^2 \)). Now we divide both the numerator and the denominator by their GCD:
\[ \frac{292 \div 4}{324 \div 4} = \frac{73}{81} \]

### Step 3: Substitute back into the square root
Now we substitute back into the square root:
\[ \sqrt{\frac{73}{81}} = \frac{\sqrt{73}}{\sqrt{81}} \]

### Step 4: Simplify the square root of the denominator
We know that \( \sqrt{81} = 9 \), so we have:
\[ \frac{\sqrt{73}}{9} \]

### Final Result
Thus, the final simplified value of the expression \( \sqrt{\frac{4 \times 73}{324}} \) is:
\[ \frac{\sqrt{73}}{9} \]

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