Mathematics

Question

Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube?

2 Answer

  • z^25 needs to be z^24 to make a perfect cube

    if z^24 then

    125x^18y^3z^24 = 5^3 (x^6)^3 y^3 (z^8)^3

  • Answer:

    [tex]z^{25}[/tex] has to be changed.

    Step-by-step explanation:

    The given monomial is [tex]125x^{18}y^{3}z^{25}[/tex].

    If we see the separate terms of the monomial then we find that each term can be written in perfect cube form except z.

    125 = 5³

    [tex]x^{18}=(x^{6})^{3}[/tex]

    y³ is in cube form

    [tex]z^{25}[/tex] is the only term which can be written in the perfect cube form if it is [tex]z^{24}=(z^{8})^{3}[/tex] or [tex]z^{27}=(z^{9})^{3}[/tex]

    So the answer is [tex]z^{25}[/tex]

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