Question

Q1 By which number 256 must be Multiply so it be a perfect cube

Q2 By which number 192 must be divided so it be a perfect cube

Q.3 Find the cube root of
A. 13824
B. 10648
C. 27000​

Answer 1

Answer:

Ans 1) 256 × 2 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 512 is a perfect cube. Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.

Ans 2) Prime factorization of 192 is: 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 23 × 23 × 3 Here, 3 is the smallest number by which 192 is divided to make it a perfect cube, i.e., 192 ÷ 3 = 64 which is a perfect cube. Thus, 3 is the required smallest number.

Ans 3) a. 13824

Ans.

13824

2×2×2×2×2×2×2×2×2×3×3×3

= 2 x 2 x 2 x 3

= 24

b. 10648

Ans.

10648

2×2×2×11×11×11

= 2 x 11

= 22

c. 27000

Ans.

27000

2×2×2×3×3×3×5×5×5

= 2 x 3 x 5

= 30

Answer 2

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