Use Prime Factorization method to find the square root of the following:-

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Question

Use Prime Factorization method to find the square root of the following:-

i . \sqrt{(1024)}

= ______

i i . \sqrt{(2025)}

= _______

Options:

A . 32, 45

B . 36, 35

C . 28, 25

D . 28, 45

Answer: Option A
:
A

1024 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2

= 2^{2} \times 2^{2} \times 2^{2} \times 2^{2} \times 2^{2} \Rightarrow \sqrt{(1024)} = \sqrt{(2^{2} \times 2^{2} \times 2^{2} \times 2^{2} \times 2^{2})} = 2 \times 2 \times 2 \times 2 \times 2 = 32

2025 = 3 \times 3 \times 3 \times 3 \times 5 \times 5

= 3^{2} \times 3^{2} \times 5^{2} \Rightarrow \sqrt{(2025)} = \sqrt{(3^{2} \times 3^{2} \times 5^{2})} = 3 \times 3 \times 5 = 45

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