Question

This is the question im stuck on. can anyone help please!!

"Can a radical ever be rational? Give examples. Justify your answer using complete sentences."

Answer 1

Yes a radical can be rational sometimes

Explanation:

If we consider the radical sign to be square root of a number and the number under the radical sign to be a square, then our radical becomes a rational. In simple words if we consider the n-th root of a number which can be written as the n-th power of another number, then the radical will become a rational. For instance sqrt 4 = 2 OR sqrt 9 = 3 etc

Answer 2

Answer: Yes, radicals can be rationals.

Explanation:

Yes, a radical can be rational.

If a square root is a perfect square, you will obtain an integer, and by definition, the integer are rationals (they can be written as simple fractions).

Example:

`√(4)=2=(2)/(1)`

If the radical has a root n and number inside of the root can be written as a power with exponent
`n`, then you will obtain a radical.

Example:

`\sqrt[3]{64}=\sqrt[3]{4^(3)}=4=(4)/(1)`