Question

The square root of 1024 is:

• A. 32
• B. 64
• C. 22
• D. 42

Hint:

Look at the units digit! The number ends in 4. For choices (A) 32 and (D) 42, the units digit squared is \(2^2 = 4\). Since \(40^2 = 1600\), 42 squared must be much larger than 1600. Hence, 32 is the only logical answer within range.

Answer 1

The Correct Option is A

Concept: The square root of a number is a value that, when multiplied by itself, gives the original number. We can solve this via prime factorization or through long division estimation.

Step 1: Using Prime Factorization method.
Let's decompose the integer number 1024 into its base prime factors by dividing consistently by 2: 1024 \div 2 &= 512
512 \div 2 &= 256
256 \div 2 &= 128
128 \div 2 &= 64
64 \div 2 &= 32
32 \div 2 &= 16
16 \div 2 &= 8
8 \div 2 &= 4
4 \div 2 &= 2
2 \div 2 &= 1 Counting the factors, we see that \(1024 = 2^{10}\).

Step 2: Computing the square root.
To find the square root, we divide the power exponent value by 2: \[ \sqrt{1024} = \sqrt{2^{10}} = 2^{\frac{10}{2}} = 2^5 \] Let us calculate the absolute product of \(2^5\): \[ 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 4 \times 4 \times 2 = 16 \times 2 = 32 \]

Step 3: Alternative validation via Option Squaring.
Let's square the given choices to find the perfect match:
• Option (A): \(32 \times 32 = 1024\)
• Option (B): \(64 \times 64 = 4096\)
• Option (C): \(22 \times 22 = 484\)
• Option (D): \(42 \times 42 = 1764\) This unambiguously confirms that the square root of 1024 is 32, pointing directly to Option (A).