Question

find the smallest number by which 17496 must be divided ,so that the quotient is a perfect cube.also find the cube root of the quotient .please give full solution

Answer 1

the smallest number by which 17496 must be divided ,so that the quotient is a perfect cube

let smallest number be x

and quotient number be y³

so, 17496/x which gives 0 as remainder and y³ as quotient

so, factors of 17496 = 2×2×2×3×3×3×3×3×3×3

no of 2's are 3
no of 3's are 7

so, factors of 17496 = 2³ × 3³ × 3³ × 3 = (2 × 3 × 3)³ × 3

so, smallest number is x = 3

y³= (2×3×3)³
y = 18

the perfect cube is y³ = 18³
cube root of 18³ = 18

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Answer 2

Answer:

Step-by-step explanation:

do prime factorisation of the no.

It will give you 2*2*2*3*3*3*3*3*3*3

So the smallest no.we will divide the number by 3.

Divide the number i e. 17496 by 3......

It will give you 5832

Prime factorisation of this number would be 2*2*2*3*3*3*3*3*3

= 2*3*3

=18 ans