Question

cube root of 13824 by division method​

Answer 1

Answer:

Hence, the cube root of 13824 is 24.

Step-by-step explanation:

Prime factorization of number 13824 is:

13824=2×2×2×2×2×2×2×2×2×3×3×3

Further we make the triplet of factors:

13824=(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)

Further simplifying the RHS and writing it in the form of a cube.

⇒13824=23×23×23×33⇒13824=29×33

Now we will proceed with finding the cube root

⇒(13824)13=(29×33)13⇒(13824)13=[(23×3)3]13⇒(13824)13=(23×3)3×13 [∵(am)n=am×n]⇒(13824)13=23×3⇒(13824)13=8×3=24

Hence, the cube root of 13824 is 24.

Answer 2

Answer:

Hence, the cube root of 13824 is 24.

24×24×24=13824

Step-by-step explanation:

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