Question

The cube root of a quotient of two perfect cubes is the -of their cube roots.

Answer 1

The cube root of a quotient of two perfect cubes is the QUOTIENT of their cube roots.

Step-by-step explanation:

Let say two perfect Cubes are

a³   & b³

quotient of two perfect cubes is  = a³/b³

The cube root of a quotient of two perfect cubes = ∛(a³/b³)

=  ∛(a/b)³

= a/b

The cube root of a quotient of two perfect cubes =  a/b

cube root of a³ =  ∛a³  = a

cube root of b³ =  ∛ b³ = b

Quotient of  cube root of a³ &  b³ = a/b

=> The cube root of a quotient of two perfect cubes  = Quotient of  cube root of a³ &  b³

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