Question

Find the cube root of each of the following numbers by prime factorisation method.
(i) 64 (ii) 512 (iii) 10648 (iv) 27000
(v) 15625 (vi) 13824 (vii) 110592 (viii) 46656
(ix) 175616 (x) 91125

Answer 1

Answer:

 

Solution:

[ prime factorization is in the attachments]

i)  64 = 2 x 2 x 2 x 2 x 2 x 2

= 2³ x 2³

³√64 =   2×2=4

ii) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 2³x 2³ x 2³

³√512 =   2×2×2=8

iii)  10648 = 2 x 2 x 2 x 11 x 11 x 11

= 2³ x 11³

³√10648 =   2×11=22

iv)  27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

= 2³ x 3³ x 5³

³√27000 =   2×3×5=30

v) 15625 = 5 x 5 x 5 x 5 x 5 x 5

= 5³x 5³

³15625 =   5×5=25

vi) 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

= 2³x 2³ x 2³ x 3³

³√13824 =   2×2×2×3=24

vii) 110592 = 2³ x 2³ x 2³ x 2³ x 3³

³√110592 =   2×2×2×2×3=48

viii) 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

= 2³ x 2³ x 3³x 3³

³√46656 =   2×2×3×3=36

ix) 175616 = 2³x 2³ x 2³ x 7³

³√175616 =   2×2×2×7=56

x) 91125 = 5³ x 3³ x 3³

³√91125 =   5×3×3=45

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