To find the square root of [tex]\(0.81\)[/tex], you can follow these steps:
Step 1: Recognize the problem involves finding [tex]\(\sqrt{0.81}\)[/tex], which means we're looking for a number that, when multiplied by itself, equals [tex]\(0.81\)[/tex].
Step 2: Start with some basic properties of square roots. Note that the square root of a perfect square is the number that, when squared, returns the original number. Here, we need the number which, when squared, gives us [tex]\(0.81\)[/tex].
Step 3: If you recognize fractions and decimal equivalents, you might remember that [tex]\(0.81\)[/tex] is [tex]\( \frac{81}{100} \)[/tex], which can be seen as [tex]\( \left(\frac{9}{10}\right)^2 \)[/tex].
Step 4: Knowing that [tex]\(0.81 = \left(\frac{9}{10}\right)^2\)[/tex], we see that the square root of [tex]\( \left(\frac{9}{10}\right)^2 \)[/tex] is [tex]\(\frac{9}{10}\)[/tex].
Step 5: Convert [tex]\(\frac{9}{10}\)[/tex] back into decimal form, which is [tex]\(0.9\)[/tex].
Therefore, the square root of [tex]\(0.81\)[/tex] is [tex]\(0.9\)[/tex].
