Question

(3) find square root by prime factorization (a) 2304 (b) 11664
plz give the answer​

Answer 1

Answer:

a) Find Square root of 2304 using prime factorization method

Solution:

First find factors of 2304

2 2304

2 1152

2 576

2 288

2 144

2 72

2 36

2 18

3 9

3 3

 1

2304=2×2×2×2×2×2×2×2×3×3

2304=2^8⋅3^2

Taking square root

∴ √ 2304  = √ (2^8⋅3^2 )

=2^4×3

=48

_____________________________________________________

b)

Find Square root of 11664 using prime factorization method

Solution:

First find factors of 11664

2 11664

2 5832

2 2916

2 1458

3 729

3 243

3 81

3 27

3 9

3 3

 1

11664=2×2×2×2×3×3×3×3×3×3

11664=2^4⋅3^6

Taking square root

∴ √ 11664 = √ (2^4⋅3^6 )

=2^2×3^3  

=108

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