The square root of 1444is :

Options

A. 33
B. 44
C. 34
D. 38

Answer

To find the square root of 1444, we can follow these steps:

### Step 1: Prime Factorization
First, we need to factor 1444 into its prime factors.

- Start by dividing 1444 by 2 (the smallest prime number):
\[ 1444 \div 2 = 722 \]

- Divide 722 by 2 again:
\[ 722 \div 2 = 361 \]

Now, we have:
\[ 1444 = 2 \times 2 \times 361 \]

### Step 2: Factor 361
Next, we need to factor 361. We can check for divisibility by prime numbers.

- 361 is not divisible by 2, 3, or 5.
- Check 19:
\[ 19 \times 19 = 361 \]

So, we can write:
\[ 361 = 19 \times 19 \]

### Step 3: Combine the Factors
Now we can combine all the prime factors of 1444:
\[ 1444 = 2 \times 2 \times 19 \times 19 \]

### Step 4: Apply the Square Root
To find the square root, we take the square root of each factor:
\[ \sqrt{1444} = \sqrt{(2 \times 2) \times (19 \times 19)} \]

This simplifies to:
\[ \sqrt{1444} = \sqrt{2^2} \times \sqrt{19^2} \]

### Step 5: Simplify the Square Roots
Taking the square root of each squared term:
\[ \sqrt{2^2} = 2 \quad \text{and} \quad \sqrt{19^2} = 19 \]

So we have:
\[ \sqrt{1444} = 2 \times 19 \]

### Step 6: Calculate the Final Result
Now we can multiply:
\[ 2 \times 19 = 38 \]

Thus, the square root of 1444 is:
\[ \sqrt{1444} = 38 \]

### Final Answer
The square root of 1444 is **38**.

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