Find the square root of 1024.

Answer

To find the square root of 1024, we can follow these steps:

### Step 1: Factorization of 1024
We start by factorizing 1024 into its prime factors. We can repeatedly divide by 2, since 1024 is an even number.

- 1024 ÷ 2 = 512
- 512 ÷ 2 = 256
- 256 ÷ 2 = 128
- 128 ÷ 2 = 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

So, we can write 1024 as:
\[ 1024 = 2^{10} \]

### Step 2: Applying the Square Root
Now that we have the prime factorization, we can find the square root. The square root of a number in the form \( a^n \) is given by \( a^{n/2} \).

Thus, the square root of 1024 can be calculated as:
\[ \sqrt{1024} = \sqrt{2^{10}} = 2^{10/2} = 2^5 \]

### Step 3: Calculating \( 2^5 \)
Now we need to calculate \( 2^5 \):
\[ 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 \]

### Conclusion
Therefore, the square root of 1024 is:
\[ \sqrt{1024} = 32 \]

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