The square root of 4356 is:
(a)84
(b)66
(c)64
(d)76

Options

A. 84
B. 66
C. 64
D. 76

Answer

To find the square root of 4356, we can use the long division method. Here’s a step-by-step solution:

### Step 1: Pair the digits
Start by pairing the digits of the number from right to left. For 4356, we have:
- Pair: 43 | 56

### Step 2: Find the largest square
Look for the largest square number less than or equal to the first pair (43). The largest square is 36 (which is \(6^2\)):
- 6 × 6 = 36

### Step 3: Subtract and bring down the next pair
Subtract 36 from 43:
- 43 - 36 = 7
Now, bring down the next pair (56) next to 7, making it 756.

### Step 4: Double the divisor
Double the number we found (6) to get 12. This will be the starting point for our new divisor:
- New divisor = 12

### Step 5: Find the next digit
We need to find a digit (let's call it \(x\)) such that:
\[ (12x) \times x \leq 756 \]
Testing with \(x = 6\):
- \(126 \times 6 = 756\)

### Step 6: Subtract and check remainder
Now, subtract 756 from 756:
- 756 - 756 = 0

### Conclusion
Since we have a remainder of 0, the square root of 4356 is:
- \(6\) (from the first pair) and \(6\) (from the second pair), which gives us 66.

Thus, the square root of 4356 is **66**.

### Answer
The correct option is (b) 66.

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