Question

Rule for roots with odd indexes (3, 5, 7)

A) They are always irrational.
B) They can be negative or positive.
C) They are always negative.
D) They are always integers.

Answer 1

The rule for roots with odd indexes is that they can be negative or positive (Option B).

Step-by-step explanation:

The rule for roots with odd indexes is that they can be negative or positive (Option B). This means that when taking the cube root (index 3), fifth root (index 5), or seventh root (index 7) of a number, the result can be positive or negative. Here are some examples:

• The cube root of 8 is 2, because 2³ = 8.
• The cube root of -8 is -2, because (-2)³ = -8.
• The fifth root of 32 is 2, because 2⁵ = 32.
• The fifth root of -32 is -2, because (-2)⁵ = -32.
• The seventh root of 128 is 2, because 2⁷ = 128.
• The seventh root of -128 is -2, because (-2)⁷ = -128.