Question

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

Answer 1

Answer:   The answer is yes.

Step-by-step explanation:  We are asked that can a radical be rational sometimes. According to the theory of real numbers, the answer here is yes. Because, if we consider the radical sign to be square root and the number under the radical sign to be a square, then our radical becomes a rational.

In other ways, we can say that 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 example,

$\sqrt{4}=2,~\sqrt{49} =7~\textup{etc.}$

$\sqrt[3]{8}=2,~\sqrt[3]{125}=5,~\textup{etc.}$

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$\sqrt[n]{b}=\sqrt[n]{a^n}=a~.~.~.$,

Thus, a radical can be a rational sometimes.

Answer 2

A radical can sometimes be radical, if the number under it was a square root. Some examples include radical 9, which would simplify to 3, and radical 64, which would simplify to 8.