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General
Easy

Question

Evaluate: cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root

hintHint:

By prime Factorize the given number and we find the cube root of the given fraction .

The correct answer is: (- 6)/7


    Explanation :-
    We know that 1728 equals 12 cubed not stretchy rightwards double arrow negative 1728 equals left parenthesis negative 1 right parenthesis cubed 1728 equals left parenthesis negative 12 right parenthesis cubed
    2744 equals 2 space cross times 1372 equals 2 cross times 2 cross times 686 equals 2 cross times 2 cross times 2 cross times 343 equals 2 cubed cross times 7 cubed equals left parenthesis 14 right parenthesis cubed
    Substituting respective values we get
    cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root equals cube root of fraction numerator left parenthesis negative 12 right parenthesis cubed over denominator left parenthesis 14 right parenthesis cubed end fraction end root equals fraction numerator negative 12 over denominator 14 end fraction equals fraction numerator negative 6 over denominator 7 end fraction

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