Question

A radical whose radicand is not a perfect power is a rational number

1. Always
2. Sometimes
3. Never true

Answer 1

Answer: 3. Never true

Step-by-step explanation
A radical number is of the form

`\sqrt[n]{x}`
where x s the radicand.

If x is of the form Mⁿ, where M is an integer, then the expression yields a rational number.
According to the question, the radicand is not a perfect power.
Therefore the expression cannot be a radical number.

Answer 2

A perfect power is a positive integer that can be expressed as an integer power of another positive integer.
More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that
`m^k = n`.

Sometimes, some fractional or decimal radicants are not perfect power, yet they evaluate to a terminating decimal or recalling decimal.

Example: 6.25 is not a perfect power, but
`√(6.25)=2.5`.

Therefore, A radical whose radicand is not a perfect power is a rational number SOMETIMES.