The square root of 1296 is :

Options

A. 33
B. 44
C. 34
D. 36

Answer

To find the square root of 1296 step by step, we can follow the prime factorization method:

### Step 1: Factor 1296
First, we will factor 1296 into its prime factors. We can start by dividing by the smallest prime number, which is 2.

- **Divide by 2:**
1296 ÷ 2 = 648
648 ÷ 2 = 324
324 ÷ 2 = 162
162 ÷ 2 = 81

At this point, we cannot divide by 2 anymore since 81 is odd.

### Step 2: Continue Factoring
Now we will factor 81, which is not divisible by 2. The next prime number is 3.

- **Divide by 3:**
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

### Step 3: Write the Prime Factorization
Now, we can write the prime factorization of 1296:
- 1296 = 2^4 × 3^4

### Step 4: Calculate the Square Root
To find the square root, we take the square root of each factor:
- √(2^4) = 2^(4/2) = 2^2 = 4
- √(3^4) = 3^(4/2) = 3^2 = 9

Now, multiply the results:
- Square root of 1296 = 4 × 9 = 36

### Final Answer
The square root of 1296 is **36**.

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