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Question

Find cube root 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

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Solution

(i) 64=2×2×2×2×2×2= 23×23=43
364=4
(ii) 512=2×2×2×2×2×2×2×2×2×2×2×2
= 23×23×23=83
3512=8
(iii) 10648= 23×113=223
310648=22
(iv) 27000= 23×33×53=303
327000=30
(v) 15625= 53×53=253
315625=25
(vi) 13824= 23×23×23×33=243
313824=24
(vii) 110592= 23×23×23×23×33=483
3110592=48
(viii) 46656= 23×23×33×33 =363
346656=36
(ix) 175616= 23×23×23×73=563
3175616=56
(x) 91125= 53×33×33 =453
391125=45

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