To solve the equation [tex]\(\square^2 = 81\)[/tex], we need to determine the number that, when squared, equals 81. Let's proceed with the solution step-by-step:
1. Understand the equation: [tex]\(\square^2 = 81\)[/tex].
This means that we need to find a number (let's call it [tex]\( x \)[/tex]) such that [tex]\( x^2 = 81 \)[/tex].
2. Isolate the variable: To find [tex]\( x \)[/tex], we take the square root of both sides of the equation.
[tex]\( x^2 = 81 \)[/tex]
Taking the square root of both sides, we get:
[tex]\( x = \sqrt{81} \)[/tex]
3. Compute the square root: The square root of 81 is 9 because [tex]\( 9 \times 9 = 81 \)[/tex].
4. Consider possible solutions: Normally, when taking the square root of a positive number, there are two possible solutions—one positive and one negative. This is because both [tex]\((+9)^2\)[/tex] and [tex]\((-9)^2\)[/tex] equal 81. However, since the problem asks for a whole number, we consider only the positive solution.
Therefore, the missing base is:
[tex]\[ x = 9 \][/tex]
The answer is 9.
