The square root of 7744 is :

Options

A. 94
B. 88
C. 77
D. None of these

Answer

To find the square root of 7744, we will follow these steps:

### Step 1: Factor the number 7744
We will start by finding the prime factors of 7744.

- First, divide by 4:
- 7744 ÷ 4 = 1936
- Divide 1936 by 4 again:
- 1936 ÷ 4 = 484
- Divide 484 by 4 again:
- 484 ÷ 4 = 121
- Now, 121 is not divisible by 4, but it is 11 × 11.

So, we can express 7744 as:
\[ 7744 = 4 \times 4 \times 4 \times 11 \times 11 \]

### Step 2: Write the factors in exponential form
We can rewrite the factors:
- \( 4 = 2^2 \), so \( 4 \times 4 \times 4 = (2^2)^3 = 2^6 \)
- \( 11 \times 11 = 11^2 \)

Thus, we can express 7744 as:
\[ 7744 = 2^6 \times 11^2 \]

### Step 3: Apply the square root
Now we apply the square root to the expression:
\[ \sqrt{7744} = \sqrt{2^6 \times 11^2} \]

Using the property of square roots:
\[ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \]
We can separate the square roots:
\[ \sqrt{7744} = \sqrt{2^6} \times \sqrt{11^2} \]

### Step 4: Simplify the square roots
Now we simplify each square root:
- \( \sqrt{2^6} = 2^{6/2} = 2^3 = 8 \)
- \( \sqrt{11^2} = 11^{2/2} = 11^1 = 11 \)

### Step 5: Multiply the results
Now we multiply the results:
\[ \sqrt{7744} = 8 \times 11 = 88 \]

Thus, the square root of 7744 is:
\[ \sqrt{7744} = 88 \]

### Final Answer:
The square root of 7744 is **88**.

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