Question

find the square root of 16384 by primefactorsation method

Answer 1

Prime Factorisation of 16384:

16384 = 2¹⁴

Find the square root of 16384:

$\sqrt{16384} = \sqrt{2^{14}} = 2^7$

Find the value of 2⁷ :

2⁷ = 128

Answer: 128

Answer 2

$\sqrt{16384}$ = 128

Given:

16384

To find:

Square root of 16384 by prime factorisation method

Solution:

To find the square root by prime factorisation we have to find the prime factors and then make a group of two two prime factors and multiply them

16384 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2

$\sqrt{16384}$ =$\sqrt{2*2*2*2*2*2*2*2*2*2*2*2*2*2}$

= $\sqrt{2^{14} }$

= (2)$^{1/2 * 14}$

(2)$^{7}$

= 128

Hence, square root of 16384 is 128.

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