Question

Find the square root of 409600 using prime factorization method

Answer 1

Answer:

The square root of 409600 = 640

Step-by-step explanation:

Given number is 409600

Required to find the square root of 409600

Solution

The prime factorization of 409600  = 2×2×2×2×2×2×2×2×2×2×2×2×2×2×5×5

= $2^{14} X 5^2$

$\sqrt{409600} = \sqrt{2^{14}X 5^2}$

= $\sqrt{(2^7 X5)^2}$

= $2^7X 5$

= 128 ×5

= 640

$\sqrt{409600} = 640$

∴ The square root of 409600 = 640

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Answer 2

Answer:

Square Root of 409600 = 640

Step-by-step explanation:

Prime factors of 409600

409600= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 5 * 5

409600 = $2^{14} * 5^2$

now we do square root of 409600

$\sqrt{409600} = \sqrt{2^{14} * 5^2}$

$\sqrt{409600} =$ $2^7 * 5$

$\sqrt{409600} =$ 128 * 5

$\sqrt{409600} =$ 640

Square Root of 409600 = 640

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