To find [tex]\(\sqrt{81}\)[/tex], follow these steps:
1. Understanding the Problem:
The square root of a number [tex]\(x\)[/tex] is a number [tex]\(y\)[/tex] such that when [tex]\(y\)[/tex] is squared ([tex]\(y \cdot y\)[/tex]), it equals [tex]\(x\)[/tex]. Mathematically, this can be written as:
[tex]\[
y = \sqrt{x}
\][/tex]
We are given [tex]\(x = 81\)[/tex], so we need to find [tex]\(y\)[/tex] such that:
[tex]\[
y^2 = 81
\][/tex]
2. Finding the Square Root:
To solve [tex]\(\sqrt{81}\)[/tex], we look for a number [tex]\(y\)[/tex] whose square is 81. Testing possible values, we find that:
[tex]\[
9 \times 9 = 81
\][/tex]
Hence, [tex]\(y = 9\)[/tex].
3. Conclusion:
Therefore, the square root of 81 is:
[tex]\[
\sqrt{81} = 9
\][/tex]
And that’s the detailed solution to the problem.
