The square root of 8836 is

Options

A. 84
B. 94
C. 96
D. 86

Answer

To find the square root of 8836, we can use the long division method for square roots. Here’s a step-by-step solution:

### Step 1: Pair the digits
Start from the right and make pairs of digits. For 8836, we can pair them as follows: (88)(36).

### Step 2: Find the largest square
Next, we need to find the largest square number that is less than or equal to the first pair (88). The squares of numbers are:
- \(8^2 = 64\)
- \(9^2 = 81\)
- \(10^2 = 100\) (too large)

The largest square less than 88 is \(9^2 = 81\).

### Step 3: Subtract and bring down the next pair
Now, subtract 81 from 88:
\[ 88 - 81 = 7 \]

Next, bring down the next pair (36) next to 7, making it 736.

### Step 4: Double the quotient and find the next digit
The current quotient is 9. Double it to get 18. Now we need to find a digit \(x\) such that:
\[ (180 + x) \cdot x \leq 736 \]

### Step 5: Trial and error for the next digit
Let’s try \(x = 4\):
\[ (180 + 4) \cdot 4 = 184 \cdot 4 = 736 \]

This fits perfectly, so \(x = 4\).

### Step 6: Combine the results
Now, we can combine the results:
The quotient so far is 94 (from 9 and 4).

### Conclusion
Thus, the square root of 8836 is:
\[ \sqrt{8836} = 94 \]

### Final Answer
The square root of 8836 is 94.

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