Answer: The smallest number by which 259875 should be divided to make it a perfect cube is 77.
Step-by-step explanation:
Let's expand the number 259875 into prime factors:
259875 = 3³ ∙ 5³ ∙ 7 ∙ 11
Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7 · 11 = 77, then the quotient is a perfect cube.
259875 ÷ 77 = 3375
[tex]\sqrt[3]{3375} =\sqrt[3]{3^{3} \cdot 5^{3} } =3 \cdot 5 = 15[/tex]
