1.

find the cube root of 64 512 10648 27000 15625 13824 8 110592 46656 175616 91125 by prime factorization method

Answer»

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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