Find the square root of `1764`.

Options

A. `52`
B. `42`
C. `32`
D. `62`

Answer

To find the square root of 1764, we can use the method of prime factorization. Here’s a step-by-step solution:

### Step 1: Factor 1764
We start by finding the prime factors of 1764. We can do this by dividing 1764 by the smallest prime number, which is 2.

1764 ÷ 2 = 882

### Step 2: Continue Factoring
Next, we continue factoring 882 by dividing it by 2 again.

882 ÷ 2 = 441

### Step 3: Factor 441
Now, we need to factor 441. Since 441 is not divisible by 2, we try the next prime number, which is 3.

441 ÷ 3 = 147

### Step 4: Factor 147
Now, we factor 147. Again, we can divide by 3.

147 ÷ 3 = 49

### Step 5: Factor 49
Next, we factor 49. Since 49 is not divisible by 3, we try the next prime number, which is 7.

49 ÷ 7 = 7

### Step 6: Complete the Factorization
Now we have:

7 ÷ 7 = 1

So, the complete prime factorization of 1764 is:

1764 = 2 × 2 × 3 × 3 × 7 × 7

### Step 7: Group the Factors
Now we can group the factors in pairs:

(2 × 2) × (3 × 3) × (7 × 7)

### Step 8: Take the Square Root
Now, we can take the square root of each pair:

√(2 × 2) = 2
√(3 × 3) = 3
√(7 × 7) = 7

### Step 9: Multiply the Results
Now, we multiply these results together to find the square root of 1764:

2 × 3 × 7 = 42

### Final Answer
Therefore, the square root of 1764 is **42**.

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