Question
Assume that $a$ is a positive integer that is not a perfect square. State whether the expression represents a rational number or an irrational number.$$\sqrt{\sqrt{81 a^{8}}}$$
Step 1
We know that $81$ is a perfect square and $a^{8}$ is a perfect square because $8$ is an even number. So, we can simplify $\sqrt{81 a^{8}}$ to $9a^{4}$. Show more…
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