To solve the expression [tex]\((\sqrt{8})^2\)[/tex], follow these detailed steps:
1. Calculate the square root of 8:
- The square root of 8 is an irrational number.
- The precise value of [tex]\(\sqrt{8}\)[/tex] is approximately 2.8284271247461903.
2. Square the result of the square root:
- Take the value obtained from the square root, which is approximately 2.8284271247461903.
- Square it to revert back to the original number under the square root.
- When squaring this value, [tex]\( (2.8284271247461903)^2 \)[/tex], you get a result slightly higher than 8, due to the floating-point arithmetic used in approximations. The result is approximately 8.000000000000002.
3. Conclusion:
- Thus, when you calculate [tex]\((\sqrt{8})^2\)[/tex], the precise outcomes are approximately 2.8284271247461903 for [tex]\(\sqrt{8}\)[/tex] and 8.000000000000002 for [tex]\((\sqrt{8})^2\)[/tex].
Therefore, the detailed solution for [tex]\((\sqrt{8})^2\)[/tex] provides you with intermediate steps leading to the final answer:
[tex]\[
(\sqrt{8})^2 = \sqrt{8} \approx 2.8284271247461903
\][/tex]
[tex]\[
(2.8284271247461903)^2 \approx 8.000000000000002.
\][/tex]
