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in Cubes And Cube Roots by (64.6k points)

Find the cube root of each of the following rational numbers:

(i) 686/-3456

(ii) -39304/-42875 

1 Answer

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Best answer

(i) 686/-3456

686/-3456 = -(∛(2×7×7×7)) / (∛(27×23))

= – (∛(2×73)) / (∛ (27×23))

= – (∛(73)) / (∛(26×23))

= – 7/(2×2×2)

= – 7/8

(v) -39304/-42875

-39304/-42875 = -(∛(2×2×2×17×17×17)) / -(∛(5×5×5×7×7×7))

= – (∛(23×173)) / -(∛(53×73))

= – (2×17)/-( 5×7)

= – 34/-35

= 34/35

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