The square root of 24025 will have _________ digits.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find out how many digits the square root of 24025 has, we can follow these steps:

### Step 1: Find the square root of 24025
We start by determining the square root of 24025.

### Step 2: Prime Factorization
We perform the prime factorization of 24025:
- Divide 24025 by 5:
\[ 24025 \div 5 = 4805 \]
- Divide 4805 by 5:
\[ 4805 \div 5 = 961 \]
- Now, we need to factor 961. We find that:
\[ 961 = 31 \times 31 \]
Thus, we can express 24025 as:
\[ 24025 = 5^2 \times 31^2 \]

### Step 3: Taking the Square Root
Now we take the square root of 24025:
\[ \sqrt{24025} = \sqrt{5^2 \times 31^2} = 5 \times 31 = 155 \]

### Step 4: Count the Digits
Now we need to determine how many digits are in the number 155.
- The number 155 has 3 digits.

### Final Answer
Thus, the square root of 24025 will have **3 digits**.

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