Question

Find the least number by which 11664 must be divided, so as to make the quotient a perfect cube. Also, find the cube root of the quotient.​

Answer 1

$Resolving \:11664 \: into \:prime \: factors, we \:get$

2| 11664

_______

2| 5832

_______

2| 2916

_______

2| 1458

_______

3| 729

_______

3| 243

_______

3| 81

_______

3| 27

_______

3| 9

_______

*** 3

11664 = 2×2×2×2×3×3×3×3×3×3

We can see that,

The prime factor 2 does not appear in a group of three factors . So, 11664 is not a perfect cube .

Hence, the smallest number which is to be divided to make it a perfect cube is 2.

$Cube \: root \: of \: 5832$

$= \sqrt[3] { 2^{3} \times 3^{3} \times 3^{3}}$

$= 2 \times 3 \times 3$

$= 18$

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Answer 2

Answer:

up ans is correct

good job