Question

what is the least number by which 43035 should be multiplied to get a perfect cube. pls solve this ​

Answer 1

Answer:

Ncert solutions

Grade 8

Mathematics

Science

Chapters in NCERT Solutions - Mathematics , Class 8

Exercises in Cubes and Cube Roots

Question 2

Q2) Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i)243

(ii)256

(iii)72

(iv)675

(v)100

Solution:

(i) 243

Prime factors of 243 =

Here 3 do not appear in 3’s group.

Therefore, 243 must be multiplied by 3 to make it a perfect cube.

(ii) 256

Prime factors of 256 = 2\times2\times2\times2\times2\times2\times2\times22×2×2×2×2×2×2×2

Here one factor 2 is required to make a 3’s group.

Therefore, 256 must be multiplied by 2 to make it a perfect cube.

(iii) 72

Prime factors of 72 = 2\times2\times2\times3\times32×2×2×3×3

Here 3 does not appear in 3’s group.

Therefore, 72 must be multiplied by 3 to make it a perfect cube.

(iv) 675

Prime factors of 675 = 3\times3\times3\times5\times53×3×3×5×5

Here factor 5 does not appear in 3’s group.

Therefore 675 must be multiplied by 3 to make it a perfect cube.

(v) 100

Prime factors of 100 = 2\times2\times5\times52×2×5×5

Here factor 2 and 5 both do not appear in 3’s group.

Therefore 100 must be multiplied by 2\times52×5= 10 to make it a perfect cube.