Solve 6¹ + 1⁶ + √81 = □²: Finding the Perfect Square Result

Let's simplify the direct calculation of the left side of the equation:

$6^1+1^6+\sqrt{81}=\textcolor{red}{☐}^2 \\ 6+1+9=\textcolor{red}{☐}^2\\ 16=\textcolor{red}{☐}^2\\$When we calculated the numerical value of the term with the exponent and the term with the root, and remembered that raising the number 1 to any power will always give the result 1,

Now let's examine the equation we got, on the left side we have the number 16 and on the right side we have a number (unknown) raised to the second power,

So we ask the question: "What number do we need to square to get the number 16?"

And the answer to that is of course - the number 4,

Therefore:

$16=\textcolor{red}{4}^2$However, since we're dealing with an even power (power of 2), we must also consider the negative possibility,

Meaning it also holds true that:

$16=\textcolor{red}{(-4)}^2$

Therefore, the correct answer is answer C.