Find the cube root of each of the following rational numbers:(i) 686/-

1.	Find the cube root of each of the following rational numbers:(i) 686/-3456(ii) -39304/-42875
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

Find the cube root of each of the following rational numbers:(i) 686/-3456(ii) -39304/-42875

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