Evaluate the following :
`(sqrt7744)/(20)`

Answer

To evaluate the expression \((\sqrt{7744})/(20)\), we will follow these steps:

### Step 1: Find the square root of 7744
To find \(\sqrt{7744}\), we can factor 7744 into its prime factors.

1. Divide 7744 by 2:
\[ 7744 \div 2 = 3872 \]
2. Divide 3872 by 2:
\[ 3872 \div 2 = 1936 \]
3. Divide 1936 by 2:
\[ 1936 \div 2 = 968 \]
4. Divide 968 by 2:
\[ 968 \div 2 = 484 \]
5. Divide 484 by 2:
\[ 484 \div 2 = 242 \]
6. Divide 242 by 2:
\[ 242 \div 2 = 121 \]
7. Now, 121 can be factored as:
\[ 121 = 11 \times 11 \]

So, the prime factorization of 7744 is:
\[ 7744 = 2^6 \times 11^2 \]

### Step 2: Calculate the square root
Using the prime factorization, we can find the square root:
\[ \sqrt{7744} = \sqrt{2^6 \times 11^2} = \sqrt{2^6} \times \sqrt{11^2} = 2^{6/2} \times 11^{2/2} = 2^3 \times 11 = 8 \times 11 = 88 \]

### Step 3: Divide by 20
Now we substitute back into the original expression:
\[ \frac{\sqrt{7744}}{20} = \frac{88}{20} \]

### Step 4: Simplify the fraction
To simplify \(\frac{88}{20}\):
1. Find the greatest common divisor (GCD) of 88 and 20, which is 4.
2. Divide both the numerator and the denominator by 4:
\[ \frac{88 \div 4}{20 \div 4} = \frac{22}{5} \]

### Final Answer
Thus, the final answer is:
\[ \frac{22}{5} \]

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