Is `196 ` a perfect square ?

Answer

To determine if 196 is a perfect square, we can follow these steps:

### Step 1: Write down the number
We start with the number 196.

### Step 2: Factor the number
We will factor 196 into its prime factors.

1. First, we divide 196 by 2 (the smallest prime number):
- 196 ÷ 2 = 98
2. Next, we divide 98 by 2 again:
- 98 ÷ 2 = 49
3. Now, we will factor 49. The smallest prime number that can divide 49 is 7:
- 49 ÷ 7 = 7
4. Finally, we divide 7 by 7:
- 7 ÷ 7 = 1

### Step 3: Write down the prime factors
The prime factorization of 196 is:
- 196 = 2 × 2 × 7 × 7
- This can also be written as:
- 196 = \(2^2 × 7^2\)

### Step 4: Check for pairs of prime factors
In the factorization \(2^2 × 7^2\):
- We have one pair of 2s (2, 2)
- We have one pair of 7s (7, 7)

### Step 5: Determine if it is a perfect square
Since all prime factors are paired (no unpaired prime factors), we conclude that 196 is a perfect square.

### Final Conclusion
Therefore, 196 is a perfect square.

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