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​

Answer 1

Answer:

4

Step-by-step explanation:

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Answer 2

Answer:

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

Step-by-step explanation:

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