By splitting into prime factors, find the square root of :
`11025`

Answer

To find the square root of 11025 by splitting it into prime factors, we can follow these steps:

### Step 1: Prime Factorization of 11025
We start by dividing 11025 by the smallest prime number, which is 2. Since 11025 is odd, it is not divisible by 2. We then try the next prime number, which is 3.

- **Dividing by 3:**
\[ 11025 \div 3 = 3675 \]

- **Dividing 3675 by 3 again:**
\[ 3675 \div 3 = 1225 \]

- **Now, we try dividing 1225 by 5:**
\[ 1225 \div 5 = 245 \]

- **Dividing 245 by 5 again:**
\[ 245 \div 5 = 49 \]

- **Finally, we divide 49 by 7:**
\[ 49 \div 7 = 7 \]

- **And divide 7 by 7:**
\[ 7 \div 7 = 1 \]

### Step 2: Collecting the Prime Factors
From the divisions, we can collect the prime factors:
\[ 11025 = 3 \times 3 \times 5 \times 5 \times 7 \times 7 \]
This can also be written as:
\[ 11025 = 3^2 \times 5^2 \times 7^2 \]

### Step 3: Finding the Square Root
To find the square root, we take the square root of each prime factor:
\[ \sqrt{11025} = \sqrt{3^2} \times \sqrt{5^2} \times \sqrt{7^2} \]
This simplifies to:
\[ \sqrt{11025} = 3 \times 5 \times 7 \]

### Step 4: Calculating the Result
Now we calculate the product:
\[ 3 \times 5 = 15 \]
\[ 15 \times 7 = 105 \]

### Final Answer
Thus, the square root of 11025 is:
\[ \sqrt{11025} = 105 \]

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